From 9a76c48d3a164ad4953f004609315cbdf137cfc7 Mon Sep 17 00:00:00 2001
From: Peter Scheiblechner <peter.scheiblechner@hslu.ch>
Date: Mon, 6 Jan 2025 12:29:11 +0000
Subject: [PATCH] 	new file:   notebooks/SW07/SW07.ipynb 	new file:  
 notebooks/SW08/SW08_bootstrap.ipynb 	new file:  
 notebooks/SW08/SW08_konfidenzintervall_t_test.ipynb 	new file:  
 notebooks/SW08/SW08_macht.ipynb

---
 notebooks/SW07/SW07.ipynb                     | 366 +++++++++++++
 notebooks/SW08/SW08_bootstrap.ipynb           | 325 ++++++++++++
 .../SW08/SW08_konfidenzintervall_t_test.ipynb | 116 +++++
 notebooks/SW08/SW08_macht.ipynb               | 486 ++++++++++++++++++
 4 files changed, 1293 insertions(+)
 create mode 100644 notebooks/SW07/SW07.ipynb
 create mode 100644 notebooks/SW08/SW08_bootstrap.ipynb
 create mode 100644 notebooks/SW08/SW08_konfidenzintervall_t_test.ipynb
 create mode 100644 notebooks/SW08/SW08_macht.ipynb

diff --git a/notebooks/SW07/SW07.ipynb b/notebooks/SW07/SW07.ipynb
new file mode 100644
index 0000000..1cb46d0
--- /dev/null
+++ b/notebooks/SW07/SW07.ipynb
@@ -0,0 +1,366 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "8f9740d2-9e9b-41f9-b79a-8c8261e9394c",
+   "metadata": {},
+   "source": [
+    "## Beispiel 10.1.2\n",
+    "Wir betrachten zwei Datensätze, bei welchen zwei Methoden zur Bestimmung der latenten Schmelzwärme von Eis verglichen werden. Wiederholte Messungen der freigesetzten Wärme beim Übergang von Eis bei $-0.7^\\circ$ C zu Wasser bei $0^\\circ$ C ergaben mit Methode A die folgenden Werte in cal/g:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "076eb7a4-fa23-47f9-8281-2f51d99482cc",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from pandas import Series, DataFrame\n",
+    "\n",
+    "methodeA = Series([79.98, 80.04, 80.02, 80.04, 80.03, 80.03, 80.04,79.97, 80.05, 80.03, 80.02, 80.00, 80.02])\n",
+    "\n",
+    "print(methodeA.mean())\n",
+    "print(methodeA.std())"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7ee362d4-2b8d-4c73-8d70-bb6ff5e7b3d5",
+   "metadata": {},
+   "source": [
+    "## Beispiel 10.1.3\n",
+    "Wir wollen neue Messreihen simulieren, die ähnlich aussehen wie die Werte in Methode A. Dazu machen wir die Annahme, dass die Messwerte in Methode A normalverteilt sind mit den wahren Parametern $\\mu = 80$ und $\\sigma^2 = 0.022$. Dann generieren wir mit `norm.rvs()` aus `scipy.stats` 6 Zufallszahlen, die dieser Verteilung folgen. Wir runden die Resultate mit `round()` von `numpy` auf zwei Nachkommastellen."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4ac20769-694a-4f35-bd54-50772dd32234",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "from scipy.stats import norm\n",
+    "\n",
+    "methodeA_sim_array = norm.rvs(size=6, loc=80, scale=0.02)\n",
+    "methodeA_sim_ger = np.round(methodeA_sim1_array, 2)\n",
+    "methodeA_sim = Series(methodeA_sim1_ger)\n",
+    "\n",
+    "print(methodeA_sim)\n",
+    "print(methodeA_sim.mean())\n",
+    "print(methodeA_sim.std())"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9db1568c-fcae-4685-b0e9-5e996b49e29f",
+   "metadata": {},
+   "source": [
+    "Führen wir dies fünfmal durch, so sehen die Resultate wie folgt aus:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "18d13c84-d486-41aa-8297-0e85b8ccd0e9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "for i in range(5):\n",
+    "    methodeA_sim = Series(np.round(norm.rvs(size=6, loc=80, scale=0.02), 2))\n",
+    "    print('Mittelwert:', np.round(methodeA_sim.mean(), 3))\n",
+    "    print('Standardabw.:', np.round(methodeA_sim.std(), 3))\n",
+    "    print()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cd6be1d2-a605-4570-8e7a-5e57107dcebf",
+   "metadata": {},
+   "source": [
+    "## Beispiel 10.1.8\n",
+    "Wir nehmen an, dass wir 6 Werte $X_1,\\ldots,X_6$ haben, die derselben Verteilung $\\mathcal{N}(\\mu,0.02^2)$ folgen. Wir nehmen zusäzlich an, dass die Zufallsvariablen unabhängig sind. Sie sind also i.i.d. Angenommen, der Mittelwert der Messwerte ist\n",
+    "$$ \\overline{X}_6=\\frac{1}{6}(X_1+\\cdots+X_6)=79.98$$\n",
+    "Unter der Annahme, dass der Erwartungswert $\\mu=80$ ist, ist die Wahrscheinlichkeit, eine *extremere Abweichung* nach unten zu erhalten,"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "655851a5-0262-4f8b-961a-83f181e2d382",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "norm.cdf(x=79.98, loc=80, scale=0.02/np.sqrt(6))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a2931a39-bed6-49bc-a7bd-7e1de59935a8",
+   "metadata": {},
+   "source": [
+    "## Verwerfungsbereich\n",
+    "Wir betrachten den zweiseitigen Hypothesentest\n",
+    "$$H_0: \\mu=80$$\n",
+    "$$H_A: \\mu\\ne 80$$\n",
+    "Den Verwerfungsbereich auf dem $5\\%$-Signifkanzniveau erhalten wir durch die beiden Quantile"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5b8c50eb-21b3-40d9-97ef-a63e5d652de2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "q_025 = norm.ppf(q=0.025, loc=80, scale=0.02/np.sqrt(6))\n",
+    "q_975 = norm.ppf(q=0.975, loc=80, scale=0.02/np.sqrt(6))\n",
+    "\n",
+    "print('Verwerfungsbereich: (-infinity,',np.round(q_025,3),']U[',np.round(q_975,3),',infinity)')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d0a2e8f3-c2a5-4b35-90ac-8f5d5d5b511d",
+   "metadata": {},
+   "source": [
+    "Da der Mittelwert $\\overline{X}_6=79.98$ im Verwerfungsbereich liegt, also **verwerfen** wir die Nullhypothese"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f46d2b7c-7f45-4b66-94cc-d5932441e1b9",
+   "metadata": {},
+   "source": [
+    "Wir können beide Quantile auch durch einen Funktionsaufruf berechnen (Vektorisierung):"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "654a75a2-56cb-49dd-a8f3-e13cc154e5b3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "q_025,q_975 = norm.ppf(q=[0.025,0.975], loc=80, scale=0.02/np.sqrt(6))\n",
+    "\n",
+    "print('Verwerfungsbereich: (-infinity,',np.round(q_025,3),']U[',np.round(q_975,3),',infinity)')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "858cacd5-a86e-4e0f-bc27-905d5e5290d2",
+   "metadata": {},
+   "source": [
+    "Wir können der Verwerfungsbereich auch mit dem Befehl `interval` berechnen:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "0bf13286-4064-4bdd-a58c-5e732bc07914",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "norm.interval(confidence=0.95, loc=80, scale=0.02/np.sqrt(6))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e6d226f1-49e6-4a5a-b21b-c86bc000ad16",
+   "metadata": {},
+   "source": [
+    "## Beispiel 10.1.15\n",
+    "Wir haben eine Stichprobe $x_1,\\ldots,x_{20}$ vom Umfang 20 einer normalverteilten Zufallsvariablen $X\\sim\\mathcal{N}(5,\\sigma_X^2)$. Wir kennen die Standardabweichung $\\sigma_X$ nicht, also schätzen wir sie aus der Stichprobe:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "386adc20-fcea-4900-bbb1-b49bd7141737",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x = Series([5.9, 3.4, 6.6, 6.3, 4.2, 2.0, 6.0, 4.8, 4.2, 2.1, 8.7, 4.4, 5.1, 2.7, 8.5, 5.8, 4.9, 5.3, 5.5, 7.9])\n",
+    "sigma_x = x.std()\n",
+    "\n",
+    "print(sigma_x)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "48a6cf7c-d4cf-4054-b0fe-fa521b28a346",
+   "metadata": {},
+   "source": [
+    "Der Mittelwert $\\overline{x}_{20}$  unserer Stichprobe ist"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b8645c0e-4c71-4af6-a81f-b948a14c8e39",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "mean_x = x.mean()\n",
+    "\n",
+    "print(mean_x)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "210e4dab-da37-4d1d-8904-23dca11ab80a",
+   "metadata": {},
+   "source": [
+    "Die Wahrscheinlichkeit, dass der Mittelwert einer Stichprobe vom Umfang 20 kleiner ist als **unserer** Mittelwert $\\overline{x}_{20}=5.215$, ist"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4bee74f5-b467-4b11-85fb-f32b53dba46b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from scipy.stats import t\n",
+    "n = x.size\n",
+    "print(t.cdf(x=mean_x, df=n-1, loc=5, scale=sigma_x/np.sqrt(n)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "eee30095-0613-4378-b0a4-1c55075a5f0e",
+   "metadata": {},
+   "source": [
+    "Alternativ kann man $\\overline{x}_{20}$ standardisieren und mit der Standard $t$-Verteilung (`loc=0` und `scale=1`) arbeiten:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2ad5d4c0-5243-4904-adca-9efb93447a7f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "t_x = (mean_x-5 ) / (sigma_x/np.sqrt(n))\n",
+    "\n",
+    "print(t_x)\n",
+    "print(t.cdf(x=t_x, df=x.size-1))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "542615c7-ea05-49a4-ab22-c6be4b555446",
+   "metadata": {},
+   "source": [
+    "Den Verwerfungsbereich für die standardisierte Teststatistik\n",
+    "$$ T = \\frac{\\overline{X}_n-\\mu_0}{\\hat{\\sigma}_X/\\sqrt{n}} $$\n",
+    "können wir mit dem $0.975$-Quantil der $t$-Verteilung berechnen:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5caf9d79-f047-4051-a91b-9e09585f1683",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "q_975 = t.ppf(q=0.975, df=12)\n",
+    "\n",
+    "print('Verwerfungsbereich: (-infinity,',-np.round(q_975,3),']U[',np.round(q_975,3),',infinity)')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "247d2d57-5c1f-4d2c-b4d0-f7174de075f2",
+   "metadata": {},
+   "source": [
+    "Unser standardisierter Wert ist \n",
+    "$$ t = \\frac{\\sqrt{6}(5.215-5)}{1.88}=0.51 $$\n",
+    "Er liegt also **nicht** im Verwerfungsbereich, daher wird die Nullhypothese $\\mu=5$ **nicht** verworfen.\n",
+    "\n",
+    "Wir können den Verwerfungsbereich aber auch direkt für $\\overline{X}_n$ mit Python berechnen:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9b965069-be05-4b56-b5fe-a879755c3671",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "t.interval(confidence=0.95, df=n-1, loc=5, scale=sigma_x/np.sqrt(n))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "babb4b90-095e-4a48-a5ca-9fd11afd23f4",
+   "metadata": {},
+   "source": [
+    "Beachten Sie, dass der erste Werte die **obere** Grenze des unteren Intervalls und der zweite Wert die **untere** Grenze des oberen Intervalls des Verwerfungsbereichs ist. Unser Mittelwert $\\overline{x}_{20}=5.215$ liegt also **nicht** im Verwerfungsbereich, daher wird die Nullhypothese $\\mu=5$ **nicht** verworfen."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5204e2e4-6da7-401e-8531-6c8d8053bd7d",
+   "metadata": {},
+   "source": [
+    "Oder wir berechnen den $p$-Wert (für den zweiseitigen Test) mit der kumulativen Verteilungsfunktion"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "490adc2a-1ec9-426b-8206-d5a4c8807086",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "p = 2*t.cdf(x=-t_x,df=n-1)\n",
+    "\n",
+    "print(p)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d953a2c8-b16d-4546-af52-81cd5f9e672e",
+   "metadata": {},
+   "source": [
+    "Wir können den $t$-Test auch direkt mit dem Befehl `ttest_1samp()` von `scipy.stats` durchführen:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b14c15de-c84e-49cc-85e8-a587c8032825",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import scipy.stats as st\n",
+    "\n",
+    "st.ttest_1samp(a=x, popmean=5)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.7"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/notebooks/SW08/SW08_bootstrap.ipynb b/notebooks/SW08/SW08_bootstrap.ipynb
new file mode 100644
index 0000000..98e798c
--- /dev/null
+++ b/notebooks/SW08/SW08_bootstrap.ipynb
@@ -0,0 +1,325 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Konstruktion Vertrauensintervall mit Bootstrap"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Die Grundidee beim Bootstrap ist, dass aus einer Messreihe durch Resampling (zufälliges Generieren von Stichproben aus dieser Messreihe) Informationen über die Messreihe gewonnen werden können, wie zum Beispiel über die Unsicherheit der Schätzung des Erwartungswertes durch den Mittelwert. \n",
+    "\n",
+    "Wir betrachten eine Messreihe, die einer unbekannten Verteilung folgt und einen unbekannten Erwartungswert $ \\mu $ hat.\n",
+    "\n",
+    "Wir nennen die unbekannte Verteilung $ F $, und wir können den Mittelwert $ \\overline{x} $ der Messreihe als Punktschätzung von $ \\mu $ betrachten. Aber wie gut ist diese Schätzung? D.h. wie gross ist die mit dieser Schätzung verbundene Unsicherheit?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Im Folgenden betrachten wir mit `Python` die Messreihe `methode_B`. Beim Bootstrap wird eine zufällige Stichprobe durch Resampling aus der Messreihe `methode_B` gewonnen. Wir nennen diese zufällige Stichprobe _bootstrap sample_.\n",
+    "\n",
+    "Das `bootstrap sample` hat dieselbe Länge $ n=8 $ wie die ursprüngliche Messreihe. Da der Standardfehler von der Länge der Messreihe abhängt, wird ein Bootstrap Sample mit derselben Länge gewählt. Wenn wir ohne Zurücklegen ziehen würden, dann käme bis auf die Reihenfolge immer die ursprüngliche Messreihe heraus. Daher ziehen wir mit Zurücklegen, es wird also jeder Wert potenziell mehrfach gezogen."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "np.random.seed(1) \n",
+    "methode_B = np.array([80.02, 79.94, 79.98, 79.97, 79.97, 80.03, 79.95, 79.97])\n",
+    "\n",
+    "# Arithmetisches Mittel der Messreihe methode_B\n",
+    "print('Arithmetisches Mittel von Messreihe Methode B:', methode_B.mean())\n",
+    "\n",
+    "# Länge n der Messreihe methode_B\n",
+    "n = methode_B.size \n",
+    "\n",
+    "# Anzahl Bootstrap samples\n",
+    "nboot = 1\n",
+    "\n",
+    "bootstrap_sample = np.random.choice(methode_B, n*nboot, replace=True)\n",
+    "\n",
+    "bootstrap_sample\n",
+    "print('Bootstrap Sample: ' , bootstrap_sample)\n",
+    "# Arithmetisches Mittel des Bootstrap Sample\n",
+    "print('Arithmetisches Mittel von Bootstrap Sample:' , bootstrap_sample.mean())"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Wir erzeugen $n_{\\rm boot}=20$ Bootstrap-Samples (Stichproben), alle mit der Länge $ n=8 $. Dies entspricht dem Ziehen eines Samples der Länge $n\\cdot n_{\\rm boot}=8\\cdot 20=160$, deren Werte wir als Matrix (zweidimensionales Array) anordnen. Jede der 20 Spalten im `bootstrap_sample_array` ist ein Bootstrap-Sample."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Anzahl Bootstrap-Samples\n",
+    "nboot = 20\n",
+    "# Die Bootstrap-Samples werden in einem array mit 20 Spalten und 8 Zeilen angeordnet\n",
+    "bootstrap_sample = np.random.choice(methode_B, n*nboot, replace=True)\n",
+    "bootstrap_sample_array = np.reshape(bootstrap_sample, (n, nboot))\n",
+    "print(bootstrap_sample_array)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Wir berechnen nun die Mittelwerte in allen Spalten und ordnen Sie der Reihen nach:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Mittelwerte der Datenpunkte entlang den Spalten werden mit Argument axis=0 berechnet\n",
+    "xbarstar = bootstrap_sample_array.mean(axis=0)\n",
+    "\n",
+    "np.sort(xbarstar)\n",
+    "print(np.sort(xbarstar))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Beim 95%-Bootstrap-Vertrauensintervall wählen wir die _mittleren_ 95% dieser Daten. Diese werden durch die 2.5%- und 97.5%-Quantile begrenzt. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ci = np.percentile(xbarstar, q=[2.5, 97.5])\n",
+    "print('Vertrauensintervall: ',ci)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Wir können auch 10000 Bootstrap-Stichproben erzeugen, womit wir wesentlich genauere Abschätzungen für das 95%-Bootstrap-Vertrauensintervall erhalten.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Anzahl Bootstrap Samples\n",
+    "nboot = 10000\n",
+    "# Wir ordnen die 10'000 Bootstrap Samples in einem array mit 10'000 Spalten an\n",
+    "bootstrap_sample = np.random.choice(methode_B, n*nboot, replace=True)\n",
+    "bootstrap_sample_array = np.reshape(bootstrap_sample, (n, nboot))\n",
+    "# Wir berechnen für jedes Bootstrap Sample den Mittelwert\n",
+    "xbarstar = bootstrap_sample_array.mean(axis=0)\n",
+    "# Wir erhalten das Vertrauensintervall, indem wir die Intervallsgrenzen der mittleren 95% \n",
+    "# der Mittelwerte betrachten\n",
+    "ci = np.percentile(xbarstar, q=[2.5, 97.5])\n",
+    "print('Vertrauensintervall: ',ci)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Interpretation von Vertrauensintervallen"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Wir simulieren nun Daten, deren wahres $ \\mu $ wir kennen. Dazu wählen wir 100 Zufallszahlen, die der Verteilung $ \\mathcal{N}(40,5^{2}) $ folgen. Das wahre $ \\mu $ ist also 40."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "\n",
+    "np.random.seed(4)\n",
+    "x = np.random.normal(loc=40,scale=5,size=100)\n",
+    "n = x.size \n",
+    "xbar = x.mean()\n",
+    "\n",
+    "# Anzahl Bootstrap-Samples\n",
+    "nboot = 20\n",
+    "\n",
+    "# Erzeuge Bootstrap-Samples\n",
+    "bootstrap_samples = np.random.choice(x, n*nboot, replace=True)\n",
+    "bootstrap_sample_array = np.reshape(bootstrap_samples, (n, nboot))\n",
+    "\n",
+    "# Arithmetisches Mittel für jedes Bootstrap Sample\n",
+    "xbarstar = bootstrap_sample_array.mean(axis=0)\n",
+    "\n",
+    "# 2.5% und 97.5% Quantile der Mittelwerte der 100 Bootstrap Samples\n",
+    "ci = np.percentile(xbarstar, q=[2.5, 97.5])\n",
+    "print(\"Vertrauensintervall: \",ci)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Wir vergleichen das Vertrauensintervall mit dem theoretisch berechneten:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from scipy.stats import t\n",
+    "import numpy as np\n",
+    "t.interval(confidence=0.95, df=n-1, loc=40, scale=np.sqrt(x.std())/np.sqrt(n))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Wir können uns nun fragen, ob das wahre $ \\mu $ nun im 95% Bootstrap-Vertrauensintervall liegt oder nicht. In unserem Fall liegt das wahre $ \\mu=40 $ in diesem Intervall. Ist dies aber immer der Fall? Wir generieren nun 100 Testreihen, wobei jede Testreihe 100 normalverteilte Zufallszahlen mit Mittelwert 40 enthält. Wir bestimmen für jede Testreihe das Vertrauensintervall und schauen, ob das wahre $ \\mu $ darin liegt. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "np.random.seed(4)\n",
+    "# Wir erzeugen 10'000 normalverteilte Zufallszahlen \n",
+    "# mit Mittelwert 40 und Standardabweichung 5\n",
+    "x = np.random.normal(loc=40, scale=5, size=10000)\n",
+    "\n",
+    "# Wir ordnen diese Zahlen in einem Array an, der aus 100 Zeilen \n",
+    "# und 100 Spalten besteht\n",
+    "measurement_array = np.reshape(x,(100,100))\n",
+    "print(measurement_array.shape)\n",
+    "print(measurement_array[1].size)\n",
+    "\n",
+    "# Anzahl Bootstrap Samples\n",
+    "nboot = 1000\n",
+    "\n",
+    "# Länge von jedem Bootstrap sample\n",
+    "n = 100\n",
+    "\n",
+    "# k zählt Anzahl Vertrauensintervalle, die das \n",
+    "# wahre mu=40 nicht enthalten\n",
+    "k=0\n",
+    "# Wir iterieren über alle 100 Testreihen und bestimmen für jede \n",
+    "# Testreihe ein Vertrauensintervall (mittels bootstrap)\n",
+    "for i in range(0,100):\n",
+    "    x = measurement_array[i]\n",
+    "    # Arithmetisches Mittel pro Zeile im Array wird berechnet\n",
+    "    xbar = x.mean()\n",
+    "    # für die Zeile x wird nun ein Vertrauensintervall\n",
+    "    # mittels Bootstrap konstruiert\n",
+    "    bootstrap_samples = np.random.choice(x, n*nboot, replace=True)\n",
+    "    bootstrap_sample_array = np.reshape(bootstrap_samples, (n, nboot))\n",
+    "    xbarstar = bootstrap_sample_array.mean(axis=0)\n",
+    "    ci = np.percentile(xbarstar, q=[2.5, 97.5])\n",
+    "    # Falls 40 im Vertrauensintervall für Zeile i NICHT enthalten ist\n",
+    "    # wird k um 1 erhöht\n",
+    "    if ci[0]<= 40 <= ci[1]:\n",
+    "        k=k+1\n",
+    "    \n",
+    "print(k)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Wir können dies auch noch graphisch darstellen. Wir bestimmen für jede Testreihe ein 95% Bootstrap-Vertrauensintervall. Zudem ist das wahre Mittel $ \\mu=40 $ eingezeichnet. Wir sehen, dass vier Vertrauensintervalle (schwarz eingezeichnet) die horizontale Linie 40 nicht schneidet. Diese Vertrauensintervalle enthalten somit das wahre Mittel _nicht_. Daher ist das wahre Mittel in 96% aller 95%-Vertrauensintervalle enthalten. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "%matplotlib inline  \n",
+    "#np.random.seed(8)\n",
+    "\n",
+    "# Wir generieren 10'000 normalverteilte Zufallszahlen\n",
+    "# mit Mittelwert 40 und Standardabweichung 5\n",
+    "x = np.random.normal(loc=40, scale=5, size=10000)\n",
+    "\n",
+    "# Wir ordnen die Zufallszahlen in einem array mit 100 Spalten\n",
+    "# und 100 Zeilen an\n",
+    "measurement_array = np.reshape(x,(100,100))\n",
+    "\n",
+    "# Anzahl Bootstrap Samples\n",
+    "nboot = 10000\n",
+    "n = 100\n",
+    "\n",
+    "# Wir iterieren über die 100 Testreihen\n",
+    "for i in range(0,100):\n",
+    "    # wir lesen die i-te Zeile aus dem measurement_array heraus\n",
+    "    y = measurement_array[i]\n",
+    "    # Bestimmung des Vertrauensintervalls der i-ten Testreihe\n",
+    "    tmpdata = np.random.choice(y, n*nboot, replace=True)\n",
+    "    bootstrapsample = np.reshape(tmpdata, (n, nboot))\n",
+    "    xbarstar = bootstrapsample.mean(axis=0)\n",
+    "    ci = np.percentile(xbarstar, q=[2.5, 97.5])\n",
+    "    plt.plot([i,i],[ci[0], ci[1]])\n",
+    "    if ~(ci[0]<= 40 <= ci[1]):\n",
+    "        plt.plot([i,i],[ci[0], ci[1]], c=\"black\",linewidth=3)\n",
+    "\n",
+    "plt.plot([-5,105],[40,40])\n",
+    "plt.show()  "
+   ]
+  }
+ ],
+ "metadata": {
+  "anaconda-cloud": {},
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.7"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/notebooks/SW08/SW08_konfidenzintervall_t_test.ipynb b/notebooks/SW08/SW08_konfidenzintervall_t_test.ipynb
new file mode 100644
index 0000000..dcabb56
--- /dev/null
+++ b/notebooks/SW08/SW08_konfidenzintervall_t_test.ipynb
@@ -0,0 +1,116 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "8bfd9df0-98c6-4a0f-ad9e-d0cc872312d2",
+   "metadata": {},
+   "source": [
+    "# Konstruktion Vertrauensintervall beim t-Test\n",
+    "\n",
+    "Das *Vertrauensinterall (Konfidenzintervall)* bei einem Hypothesentest beinhaltet alle Werte der Teststatistik, bei denen die Nullhypothese **nicht** verworfen wird. Das sind also alle Werte des Parameters in der Nullhyothese, die als verträglich mit den gegebenen Daten angesehen werden. Mit anderen Worten ist es das Intervall, in dem der  Wert des wahren Parameters mit hoher Wahrscheinlichkeit liegt. Der Wert dieser Wahrscheinlichkeit ist dabei $1-\\alpha$, wobei $\\alpha$ das Signifikanzniveau ist.\n",
+    "\n",
+    "Bei einem $t$-Test geht man von $n$ unabhängigen Messwerten aus, die alle der gleichen Verteilung folgen:\n",
+    "$$ X_1,\\ldots,X_n \\sim \\mathcal{N}(\\mu,\\sigma^2) $$\n",
+    "Hierbei ist $\\mu$ der unbekannte Erwartungswert und $\\sigma$ die unbekannte Standardabweichung. Die Standardabweichung wird aus den Daten geschätzt:\n",
+    "$$ \\hat{\\sigma}^2 = \\frac{1}{n-1}\\sum_{i=1}^n (X_i-\\overline{X}_{n})^2 \\qquad \\text{und}\\qquad \\hat{\\sigma}=\\sqrt{\\hat{\\sigma}^2}$$\n",
+    "Das zweiseitige $(1-\\alpha)$-Vertrauensintervall kann man wie folgt berechnen:\n",
+    "$$ I=\\left[\\overline{X}_n - t_{\\rm krit}\\cdot \\frac{\\hat{\\sigma}}{\\sqrt{n}}, \\overline{X}_n + t_{\\rm krit}\\cdot \\frac{\\hat{\\sigma}}{\\sqrt{n}}\\right]$$\n",
+    "Hierbei ist $t_{\\rm krit}$ der *kritische $t$-Wert*, welcher beim zweiseitigen Test das $(1-\\frac{\\alpha}{2})$-Quantil der $t$-Verteilung mit $n-1$ Freiheitsgraden ist."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "35eea096-c4de-457b-a73e-6a4880a4ba48",
+   "metadata": {},
+   "source": [
+    "## Beispiel: Schmelzwärme\n",
+    "\n",
+    "Wir betrachten als Beispiel die Messreihe der Schmelzwärme mit Methode A. Wir schätzen $\\mu$ und $\\sigma$ aus den Daten."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "da067d25-b627-429f-ac6f-ebb120c3b93b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "from pandas import Series\n",
+    "from scipy.stats import t\n",
+    "\n",
+    "x = Series([79.98, 80.04, 80.02, 80.04, 80.03, 80.03, 80.04,\n",
+    "            79.97, 80.05,80.03, 80.02, 80.00, 80.02])\n",
+    "n = x.size\n",
+    "alpha=0.05\n",
+    "x_bar = x.mean()\n",
+    "sigma_hat = x.std()\n",
+    "print(\"n: \", n)\n",
+    "print(\"x_bar: \", np.round(x_bar,4))\n",
+    "print(\"sigma_hat: \",np.round(sigma_hat,4))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4d62eb64-0428-4065-977f-bdcac1a494c3",
+   "metadata": {},
+   "source": [
+    "Wir berechnen den kritischen $t$-Wert und das Konfidenzintervall mit obigen Formeln."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6482d887-cd47-476e-983d-89982654ad1a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Vertrauensintervall (Konfidenzintervall)\n",
+    "t_crit = t.ppf(q=1-alpha/2, df=n-1)\n",
+    "print(\"Kritischer t-Wert: \", np.round(t_crit,4))\n",
+    "I = x_bar+np.array([-1,1])*t_crit*sigma_hat/np.sqrt(n)\n",
+    "print(\"Konfidenzintervall: \", np.round(I,4))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "88a5eaca-2c60-40c0-a05d-8fc068bfcbd0",
+   "metadata": {},
+   "source": [
+    "Alternativ kann man das Konfidenzintervall auch bequem mit einem Befehl berechnen:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "bb770364-215d-45d4-ad3b-94e86b205322",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "I = t.interval(confidence=1-alpha, df=n-1, loc=x_bar, scale=sigma_hat/np.sqrt(n))\n",
+    "print(np.round(I,4))"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.7"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/notebooks/SW08/SW08_macht.ipynb b/notebooks/SW08/SW08_macht.ipynb
new file mode 100644
index 0000000..54886d3
--- /dev/null
+++ b/notebooks/SW08/SW08_macht.ipynb
@@ -0,0 +1,486 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Macht\n",
+    "\n",
+    "## Fehler 1. Art und 2. Art\n",
+    "\n",
+    "Hypothesentests geben keine absolute Sicherheit zur Überprüfung einer Aussage, sondern nur mit einer bestimmten Wahrscheinlichkeit, meist zu 95%, wenn das Signifikanzniveau $\\alpha=0.05$ ist.\n",
+    "\n",
+    "Was man _will_ , ist folgendes:\n",
+    "\n",
+    "- Die Nullhypothese stimmt in Wahrheit und sie wird durch die Daten nicht verworfen.\n",
+    "- Die Nullhypothese stimmt in Wahrheit nicht und sie wird durch die Daten verworfen.\n",
+    "\n",
+    "Allerdings sind auch folgende Fälle möglich:\n",
+    "- Die Nullhypothese stimmt in Wahrheit, aber sie wird durch die Daten (fälschlicherweise) verworfen. Dies nennt man Fehler 1. Art.\n",
+    "- Die Nullhypothese stimmt in Wahrheit nicht, aber sie wird durch die Daten (fälschlicherweise) nicht verworfen. Dies nennt man Fehler 2. Art.\n",
+    "\n",
+    "Wir wollen diese Fehler genauer graphisch untersuchen und gehen dabei von der Normalverteilungskurve $X\\sim\\mathcal{N}(5,2^2)$ aus, das heisst $\\mu_0=5$ und machen einen einseitigen Test nach oben. \n",
+    "\n",
+    "### Fehler 1. Art\n",
+    "Der Fehler 1. Art wird dann gemacht, wenn die Nullhypothese durch die Daten verworfen wird, obwohl die Nullhypothese stimmt. Das heisst, $\\overline{x}_n$ liegt im Verwerfungsbereich. Dies wiederum entspricht gerade dem Signifikanzniveau $\\alpha=0.05$. Der Fehler 1. Art entspricht gerade dem Signifikanzniveau. Mit dieser Wahrscheinlichkeit verwerfen wir die Nullhypothese, obwohl sie stimmt. Die Wahrscheinlichkeit können wir auch einzeichnen und entspricht der roten Fläche."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f08d8bec7c0>]"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<Figure size 2000x500 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "%matplotlib inline \n",
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "import matplotlib.pyplot as plt\n",
+    "from scipy.stats import norm\n",
+    "plt.rc('text', usetex=True)\n",
+    "plt.rcParams[\"figure.figsize\"] = (20,5)\n",
+    "\n",
+    "# Bereich der x-Achse\n",
+    "aw = 0\n",
+    "ew = 22\n",
+    "\n",
+    "# Berechnung der Funktionswerte\n",
+    "mean = 5\n",
+    "sd = 2\n",
+    "\n",
+    "x = np.linspace(start=aw, stop=ew, num=100)\n",
+    "y = norm.pdf(x, loc=mean, scale=sd)\n",
+    "\n",
+    "plt.plot(x, y)\n",
+    "\n",
+    "\n",
+    "\n",
+    "#Bestimmung der Quantile\n",
+    "q_95 = norm.ppf(q=0.95, loc=mean , scale=sd)\n",
+    "\n",
+    "x_v = np.linspace(q_95, ew, 500)\n",
+    "\n",
+    "# Fehler 1. Art\n",
+    "\n",
+    "plt.text(q_95, -.03, r\"$q_{0.95}$\", fontsize=20, ha=\"center\")\n",
+    "plt.fill_between(x_v, norm.pdf(x_v, loc=5, scale=2), color=\"red\")\n",
+    "plt.plot([aw, ew], [0,0], color=\"black\", linewidth=1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Fehler 2. Art\n",
+    "Beim Fehler 2. Art wird die Nullhypothese _nicht_ verworfen, obwohl die Nullhypothese nicht richtig ist. Oder anders gesagt: Die Alternativhypothese ist richtig, die Nullhypothese wird durch die Daten nicht veworfen. \n",
+    "\n",
+    "Auch diesen Fehler können wir in die Graphik einzeichnen, dazu brauchen wir aber das $\\mu_A$ der Alternativhypothese, da diese ja richtig ist. Nehmen wir $\\mu_A=10$: "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f22c3d583d0>]"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 1440x360 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "y_A = norm.pdf(x, loc=10, scale=2)\n",
+    "\n",
+    "plt.plot(x, y)\n",
+    "plt.plot(x, y_A)\n",
+    "\n",
+    "plt.fill_between(x_v, norm.pdf(x_v, loc=5, scale=2), color=\"red\")\n",
+    "plt.text(q_95, -.03, r\"$q_{0.95}$\", fontsize=20, ha=\"center\")\n",
+    "plt.plot([aw, ew], [0,0], color=\"black\", linewidth=1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Nun wird die Nullhypothese _nicht_ verworfen, dann liegt $\\overline{x}_n$ links des roten Bereiches. Nun betrachten wir die Wahrscheinlichkeit, dass die Alternativhypothese _richtig_ ist, aber trotzdem nicht angenommen wird. Das heisst, wir gehen von der Alternativhypothese aus und betrachten den Bereich der Alternativhypothese, die nicht im Verwerfungsbereich der Nullhypothese liegt. Dies entspricht dann der Wahrscheinlichkeit des Fehlers 2. Art, die unten eingezeichnet violett (eigenlich \"plum\") eingezeichnet ist.  "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Text(8.289707253902945, -0.03, '$q_{0.95}$')"
+      ]
+     },
+     "execution_count": 43,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 1440x360 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.plot(x, y)\n",
+    "plt.plot(x, y_A)\n",
+    "\n",
+    "x_2 = np.linspace(aw, q_95, 500)\n",
+    "x_v = np.linspace(q_95, ew, 500)\n",
+    "\n",
+    "plt.fill_between(x_v, norm.pdf(x_v, loc=5, scale=2), color=\"red\")\n",
+    "plt.fill_between(x_2, norm.pdf(x_2, loc=10, scale=2), color=\"plum\")\n",
+    "\n",
+    "plt.text(q_95, -.03, r\"$q_{0.95}$\", fontsize=20, ha=\"center\")\n",
+    "plt.plot([aw, ew], [0,0], color=\"black\", linewidth=1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In Abbildung oben haben wir die beiden Fehler eingezeichnet: \n",
+    "- Rot: Fehler 1. Art\n",
+    "- Plum: Fehler 2. Art\n",
+    "Man beachte: Die Grenzlinie wird immer durch $q_{0.95}$ von $H_0$  bestimmt:\n",
+    "- Beim Fehler 1. Art betrachten wir die Fläche unter der Kurve der Nullhypothese rechts der Grenze.\n",
+    "- Beim Fehler 2. Art betrachten wir die Fläche unter der Kurve der Alternativhypothese links der Grenze.\n",
+    "\n",
+    "## Macht\n",
+    "\n",
+    "Nun sind wir aber an der Wahrscheinlichkeit interessiert, dass die Alternativhypothese richtigerweise angenommen wurde. Diese Wahrscheinlichkeit nennen wir _Macht_. Auch diese können wir in die Graphik einzeichnen. \n",
+    "\n",
+    "Das heisst, $\\overline{x}_n$ liegt nun im Verwerfungsbereich der Nullhypothese und wir gehen aber von der Alternativhypothese aus. Wir betrachten also den Bereich unter Kurve der Alternativhypothese rechts der Grenze $q_{0.95}$. Dies ist dann die Macht (unten grün eingezeichnet)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f22c3cc2b90>]"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 1440x360 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.plot(x, y)\n",
+    "plt.plot(x, y_A)\n",
+    "\n",
+    "plt.fill_between(x_v, norm.pdf(x_v, loc=10, scale=2), color=\"limegreen\")\n",
+    "plt.text(q_95, -.03, r\"$q_{0.95}$\", fontsize=20, ha=\"center\")\n",
+    "plt.plot([aw, ew], [0,0], color=\"black\", linewidth=1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Offensichtlich gilt:\n",
+    "$$\n",
+    "\\text{Macht}\n",
+    "=1-\\text{Fehler 2. Art}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Wir definieren noch eine Funktion power(), die die Macht für verschiedene $\\mu_A$ einzeichnet:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def power(mean_A):\n",
+    "    plt.plot(x,y)\n",
+    "    y_A = norm.pdf(x, loc=mean_A, scale=2)\n",
+    "    plt.plot(x, y_A)\n",
+    "    plt.fill_between(x_v, norm.pdf(x_v, loc=mean_A, scale=2), color=\"limegreen\")\n",
+    "    plt.text(q_95, -.03, r\"$q_{0.95}$\", fontsize=20, ha=\"center\")   \n",
+    "    plt.plot([aw, ew], [0,0], color=\"black\", linewidth=1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Wir wählen nun $\\mu_A=7$, dann $\\mu_A=10$ und $\\mu_A=12$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 1440x360 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "power(7)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 1440x360 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "power(10)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 1440x360 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "power(12)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Wer sehen also, je weiter die Alternativhypothese von der Alternativhypothese entfernt ist, umso grösser ist die Macht, das heisst die Wahrscheinlichkeit, die Nullhypothese richtigerweise verworfen zu haben. Und so sollte es ja auch so sein. \n",
+    "\n",
+    "\n",
+    "## Macht und Signifikanzniveau\n",
+    "\n",
+    "Wir wählen wieder $\\mu_0=5$ und $\\mu_A=10$. Diese lassen wir fest und untersuchen, welchen Einfluss das Signifikanzniveau auf die Macht und dementsprechend auf den Fehler 2. Art hat. \n",
+    "\n",
+    "Dazu definieren wir die Funktion power_alpha():"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def power_alpha(alpha):\n",
+    "    plt.plot(x,y)\n",
+    "    conf = 1-alpha\n",
+    "    y_A = norm.pdf(x, loc=10, scale=2)\n",
+    "    plt.plot(x, y_A)\n",
+    "    q_alpha = norm.ppf(q=1-alpha, loc=5, scale=2)\n",
+    "    x_v = np.linspace(q_alpha, ew, 500)\n",
+    "    plt.fill_between(x_v, norm.pdf(x_v, loc=10, scale=2), color=\"limegreen\")\n",
+    "    plt.text(q_alpha, -.03, r\"$q_{1-\\alpha}$\", fontsize=20, ha=\"center\")  \n",
+    "    plt.fill_between(x_v, norm.pdf(x_v, loc=5, scale=2), color=\"red\")\n",
+    "    plt.plot([aw, ew], [0,0], color=\"black\", linewidth=1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Wir wählen $\\alpha=0.1$, $\\alpha=0.05$, $\\alpha=0.01$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<Figure size 2000x500 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "power_alpha(.1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 1440x360 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "power_alpha(0.05)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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7SURERKTWVTssMsaMNMYMNMbceYjXBxpjZu/3uK8xZoMxZknVP09WPb9n/8ci0rhl7y3lqrcXUFRWwYd/P5520cG2k5ocl8vw9MW9OCsxjgenrWTasm22k6QxSF8A0/4J7U6GIc+BljDWuowQf24/rgXxBYVs/vA03BUltpNEREREatVhh0XGmJEAjuPMAXKNMQMPfE/Va/uLchyno+M4/YBrgPFVz1/sOE4/x3HuqoVuEbGotMLNPz5YTGZ+Ke/+7TgSm4fZTmqy/HxcvPKnvhzXPorbJi5n8eYc20nSkO3ZXLmhdXgbuPRD8NWy0LryW0wQj/aKo9vOnaz47NzKPaJEREREmojqriw6DthY9fVGoG91BzxgeJTgOM6+z0cYYxKOPFFEGprRX6xieUYuz13ai37tomznNHmBfj68eVV/WkUG8c+PfiNrr65ikIMoyYOPLwVPBVwxEZrpe7OuTW8bxrudIuizZinL5l5rO0dERESk1lQ3LIo44HF0TQ9sjBnlOM6k/Z6KAnKMMeMP9X5jzGJjzOLs7OyankZE6tnERRl8sjCd607ryLlJLWzneI3wZn68fmU/8kvK+fdHSyl3e2wnSUPiroDP/gq711deURTTyXaR13ilWzRzWgTT88cJrFv2ku0cERERkVpR3bAol8ohz9EYtP8Dx3HecBwnl8rlbCMPfHPV6/0dx+kfGxt7lKcUkbq0Ymsu909byUmdorn97C62c7xOtxZhPHFhTxZuzuHxmWm2c6ShcBz4+i7Y8C0MeR46nGq7yKs4xvBQn3hWRwTQavqDZKbPtZ0kIiIicsyqGxYt4r9XFyUAsw/z3t8ZYyIOeDxqvwHR7iMqFJEGIaewjOv/8xsxwf68eFkffH10M0UbLujTir+e2J53ftqkDa+l0oLxsOgtOOkm6HuV7RqvVOLr4tbjW5Dv58L1yeUU5262nSQiIiJyTA77217VMrKEfRtb79uP6IC7n40E+h9wtVAUsP8urBPZb4PsA5aniUgD5/Y43PjJUrL3lvLalf2IDgmwneTV7ju/G8e1j+Tuz1NI25lvO0dsWjsLZt0DiUPgrNG2a7zarkBfbjmhBcFlZWR/cCZOWaHtJBEREZGjVu2lAY7jPOU4zhzHcd7Y77lB+309yXGcyP0HQI7jbHQc59r9HudWHWOO4zhP1eYfQETq3rhv1vDj+l2MGd6DXm0O3MpM6pufj4tXruhLSKAv1324hLzicttJYkP2Wph0NTRPhgvfAJeu9rNtbXgA9/ZrTuuc3WyacL7ukCYiIiKNln6yFJHDmpW6k1fnb+Cy49pw2fFtbedIlbiwQF77U1+27inmtonL8Hj0S6lXKS+u3NDaNxAu/xT8g20XSZUfmgfzSrdoEjYsZdNPD9nOERERETkqGhaJyCFtyC7gtonL6dk6nNHDetjOkQP0bx/F/ed3Y87qLF6Zt952jtSnWfdCViqMGA9hLW3XyAHe7xTBz7HNaPnti+ze+r3tHBEREZEjpmGRiBxUYWkF1324BH9fF69d2Y9APx/bSXIQfzmxPRf0bsmzc9Yyf02W7RypD6lTYPE7cOKN0Hmg7Ro5CMcYHuwbx14/FyUTLqO8NNd2koiIiMgR0bBIRP7AcRzunLSCDdkFvHR5H1pFBNlOkkMwxvD4hT3pGh/KTZ8uIyOnyHaS1KU9m+GLm6BVfzjrQds1chh7Any5v288LfYWsnrSMNs5IiIiIkdEwyIR+YO3ftjElyk7uOOcRE7qFGM7R6oR5O/D+Kv64TgO1364hJJyt+0kqQvucpj098qvR74NPn52e6Rai2Kb8U6XSHquW07qL6Nt54iIiIjUmIZFIvI/ftmwmye+TuPcHs257rQE2zlSQ+2ig3n+st6s2pHPfVNW4uguTE3P3DGwbTEMexEi29uukRp6o0sUS6MC6TD3BbJ2/GI7R0RERKRGNCwSkd/tKijlhk+W0j66GU9f3BNjjO0kOQJnJsZz01md+fy3rXy2eKvtHKlN62bDzy9C/6uhxwW2a+QIuF2G+/rFU2agYOIllJcX2E4SERERqZaGRSICVO5TdPfnKeQXl/PKn/oSGqglLo3RTWd1ZkBCNA9PTyV9t/YvahLyd8CUayE+Cc55zHaNHIXMID8e7hNPwp58Vky90HaOiIiISLU0LBIRACYsymDO6kzuPLcric3DbOfIUXK5DOMu6YXLZbhl4jIq3B7bSXIsPG6YfA2UF8PId8BPm803Vt83D+bjhHD6pS5gzdLnbeeIiIiIHJaGRSLC5l2FjJmxihM7RnP1SR1s58gxahkRxNgLkliyZQ+vzd9gO0eOxQ/jYPMPMPhpiO1qu0aO0YvdYlgdHkDzmWPI3Z1qO0dERETkkDQsEvFyFW4PN09Yhu9+V6RI4ze8dyuG9WrJC3PXsWJrru0cORqbf4L5j0PyJdD7T7ZrpBaU+xju6RePr8dh16fDcNzltpNEREREDkrDIhEv98q8DSzLyGXsiGRahGuJS1PyyPAkYkMDuPnTZRSVVdjOkSNRlAOf/wMiO8CQZ0GbzTcZGSH+PNYrlk7Zu1g188+2c0REREQOSsMiES+2LCOXF79dx/DeLRnWq6XtHKll4c38GHdxLzbuKuSxmatt50hNOQ5MvR6KdlXuUxQQartIatnXrUOZ2jaUbktmsmP1p7ZzRERERP5AwyIRL1VUVsEtE5YRHxrAmOFJtnOkjpzYKYZ/nNyB//yazry0LNs5UhML34S1X8OgR6Blb9s1UkeeToplc4g/AdNuoLwg03aOiIiIyP/QsEjES439cjWbdxcy7pLehAf52c6ROnT7OV1JbB7KHZNWsLug1HaOHM7uDTD7Qeg0CE641naN1KESXxf39osnrLSMDVMutJ0jIiIi8j80LBLxQnNXZ/LxgnSuOSWBAR2jbedIHQv08+G5S3uTX1zOPZNTcBzHdpIcjMcNU/8Jvv4w7EXtU+QF1oUH8GaXKBI3rGTjb8/bzhERERH5nYZFIl5mV0Epd32+gsTmodx2dhfbOVJPurUI445zuvLNqkwmLs6wnSMHs+B1yPgVzn0SwrSHmLd4r3Mkq8MDiJr1CIX56bZzRERERAANi0S8iuM43P15CvklFTx/WW8CfH1sJ0k9+vvJHRiQEM3D01exZXeh7RzZ3651MHcMdDkPel1mu0bqUYXL8FCfOILLKtg0WcvRREREpGHQsEjEi0xYlMGc1ZnceU5XEpuH2c6ReuZyGcZd0gsfl+GWCcuocHtsJwlULT+7HnwDYejzWn7mhTaEBTA+MYqkzetIW/i47RwRERERDYtEvMXmXYWMmbGKkzpFc/VJHWzniCUtI4IYe0ESv6Xn8ur8DbZzBOCXl2HrIhj8DIQ2t10jlnzQMZKVEQG0mPM0e3P1vSkiIiJ2aVgk4gUq3B5umbgMX5fhmYt74XLpygVvNrx3K4b1askLc9exPCPXdo53y0qDbx+FxCGQPNJ2jVjkdhlG94knsMLD5s8vBG1ELyIiIhZpWCTiBd76cRNL03MZOyKZFuFBtnOkAXhkeBJxoQHc/tlySivctnO8k7uicvmZfzAMeU7Lz4RNof68lhhFcsZmUn992HaOiIiIeDENi0SauI3ZBTw3ey3n9IhnaM8WtnOkgQhv5sejI5JYl1XAK/O05MWKn1+A7b/B+eMgJM52jTQQH3WMYEVkAG2+fZG8PWts54iIiIiXqnZYZIwZaYwZaIy58xCvDzTGzD7guT3GmCXGmCdrehwRqX0eT+XdzwJ8XTwyPAmjKxdkP2cmxnNB75a8Om89q3fk287xLpmpMO9x6H4BJOkOWPJfHlO5HM3f7WHr5yO1HE1ERESsOOywyBgzEsBxnDlArjFm4IHvqXrtQBc7jtPPcZy7anocEal9Hy1MZ+HmHO4f0p24sEDbOdIAPTi0B+FBftz1+QrdHa2+uMsrl58FhldeVSRygC0h/rzSLZoeW9NZ9ctDtnNERETEC1V3ZdFxwMaqrzcCfWt43AhjTEItHEdEjtK23GKemLmaUzrHcHG/1rZzpIGKCvZn9LAerNiaxzs/bbKd4x1+fB52LIchz0JwjO0aaaA+TQhnaVQgbea9TH6OlqOJiIhI/apuWBRxwOPoGh43Csgxxoyv6XGMMaOMMYuNMYuzs7NreBoRORjHcbhvSgoO8NiIZC0/k8Ma0rMFg7rHM+6btWzaVWg7p2nbmQLfPQlJI6H7cNs10oB5jGF07zj8PB62aTmaiIiI1LPqhkW5VA5+jojjOG84jpNL5ZKzkTU5TtVn+juO0z82NvZITyki+5m6bBvz12RzxzldaRPVzHaONHDGGMZekIS/r4u7P1+Bx6NfSutERVnl8rOgSBj8tO0aaQS2hvjzUrdoum1LZ90vo23niIiIiBepbli0iP9eFZQAzD7Me4HfrxAaWfVw99EeR0SOTvbeUh6evoq+bSP484D2tnOkkYgPC+T+87uxYFMOHy9Mt53TNP0wrvLKoqHPQ7Mj/nsY8VITOoSzJDqQFt++RFHOWts5IiIi4iUOOyxyHGcSkLBvQ+p9m1nvf/ezqsFQ//0GRBPZbxNrx3EmHeo4IlL7Rk9PpajUzVMje+Lj0vIzqblL+rfhpE7RPPFVGttzi23nNC1ZqyuHRcmXQOL5tmukEXGM4eHe8fg6HjKmXKrlaCIiIlIvqruyCMdxnnIcZ47jOG/s99yg/b6e5DhOZNVACMdxcqveP8dxnKcOdxwRqV2zUnfy5Yod3HhWJzrFhdrOkUbGGMPjI3ri9lTteaVfSmuHxwPTb4KAUDj3cds10ghtC/bj9a5RdM3YyKbfnredIyIiIl6g2mGRiDQOeUXl3D91Jd1ahHHtaR1t50gj1Ta6Gbef05V5a7KZtmy77ZymYck7kLEAznlMdz+To/ZxQgRp4QGEz36U0qIs2zkiIiLSxGlYJNJEPDpzFTmFZTw9sid+PvrWlqP31xPb06dtBA9PT2VXQantnMYtfzvMHg0Jp0OvyyzHSGPmdhke6RVLeEk5a7/Q/5ZERESkbuk3SpEm4Md1u5i4eCujTk0gqVW47Rxp5Hxchqcu6klhqZvRX6TazmncZt4BngoY8hwY7SEmxyYtIpBPEiJITltCxpqJtnNERESkCdOwSKSRKyqr4O7JK0iICeamszrbzpEmonN8KDec2YkZK3bwTepO2zmN0+rpkDYDTr8bohJs10gT8VpiFNuDfDEzbsZdXmQ7R0RERJooDYtEGrmnZ61h655inrioJ4F+PrZzpAm57vSOJDYP5f6pK8krLred07iU5FVeVRSfDAP+ZbtGmpASXxeP9Yql9d5CVn59te0cERERaaI0LBJpxJZs2cN7P2/mzwPacXyHKNs50sT4+bh4emQvdhWU8vjM1bZzGpc5D0NBJgx7AXz8bNdIE/NLXDBftQqh+29fk7XtB9s5IiIi0gRpWCTSSJW7Pdw7OYXmYYHceW6i7RxpopJbh3PNKQl8uiiDBRt3285pHNJ/hcVvwwnXQat+tmukiRqXFEORryFv6l9xPG7bOSIiItLEaFgk0ki99cMm1mTuZczwJEICfG3nSBN208DOtI4M4r6pKymr8NjOadgqSmH6TRDeBs64z3aNNGF7Anx5rkcMnbN3seqHO23niIiISBOjYZFII5SRU8QLc9dyTo94BnWPt50jTVwzf18eGZ7E+qwC3vh+g+2chu2nFyA7Dc5/FgJCbNdIEze9TSgLY4Jo98M77N2z1naOiIiINCEaFok0Mo7jcP/UlfgYw+hhPWzniJc4IzGO85Nb8OK369m8q9B2TsOUvRa+fxp6XAhdzrZdI97AGB7tGYuvxyF96mW2a0RERKQJ0bBIpJH5MmUH363N5razu9IiPMh2jniRB4d2J8DHxf1TV+I4ju2chsXjqVx+5hcE5z1pu0a8yNYQf97qGkmPLRvYuOwl2zkiIiLSRGhYJNKI5BWX8/D0VSS3CucvJ7a3nSNeJj4skDvP7cqP63cxbdl22zkNy9IPIP1nOHsshMTZrhEv82HHSNaF+hM2awzlxTm2c0RERKQJ0LBIpBF5ZtYadheU8tiIZHxcxnaOeKErTmhHrzYRjP1yFblFZbZzGoa9O+GbB6HdydDnKtu+E2tgAAAgAElEQVQ14oUqXIaxveOIKi4jbcafbOeIiIhIE6BhkUgj8Vv6Hv6zYAt/PbEDya3DbeeIl/JxGR4bkcSeonKe/DrNdk7D8NVdUFECQ18AoyGu2LEyMpAJHcLpkfozmRum284RERGRRk7DIpFGoNzt4d7JKTQPC+TWs7vYzhEv16NlOH8/uQOfLMxg0WYvX/Ky9htYNRVOvR1iOtmuES/3ardosgN9KfvinzgVuvJPREREjp6GRSKNwDs/biJt515GD+tBSICv7RwRbh7YmVYRQdw7OYWyCo/tHDvKimDm7RDTBU66yXaNCEW+Lp5KjqFNXj6r591sO0dEREQaMQ2LRBq4jJwinpuzlkHd4zmnR3PbOSIANPP3ZczwHqzLKuDNHzbazrHjh2cgdwuc/yz4BtiuEQFgfvNgvotvRvtfP2Hv7tW2c0RERKSR0rBIpAFzHIcHp63EZQwPD+thO0fkf5zVLZ7zkprz4tx1bNldaDunfmWlwU8vQq/LocMptmtE/ssYnkqOxeCwdeoVtmtERESkkdKwSKQB+2rlTuatyea2s7vSMiLIdo7IHzw0tAd+Pi7un7oSx3Fs59QPx4EZt4B/MJw91naNyB/sbObH+K5RdMvYyKZlL9vOERERkUZIwyKRBiq/pJzRX6TSo2UYfxnQznaOyEE1Dw/kjnO68sO6XXyxfLvtnPqx7GNI/xkGjYHgGNs1Igf1SUIE60P9CZk1hvLSPbZzREREpJHRsEikgXpm1hp2FZTy+IXJ+ProW1Uariv/rx09W4fzyIxV5BWV286pW0U58M390OYE6HOV7RqRQ6pwGR7rGUtscSmrZ/7Ndo6IiIg0MvoNVKQBWpaRy4e/buHPA9rTs3WE7RyRw/JxGR4bkUxOYRlPzkqznVO3Zj8Apfkw5Dlw6T+h0rAtjw5iStswuq+YR3bGfNs5IiIi0ojoJ12RBqbC7eHeySnEhwZy29ldbOeI1EhSq3CuPqkDHy9IZ8mWHNs5dWPLz7D0PzDgXxCvDeelcXixezR7/XzIn/Z38Hhs54iIiEgjUe2wyBgz0hgz0Bhz5yFeH2iMmb3f44iqz4w0xjy53/N7jDFL9n9ORP7o/V+2sGpHPg8N7U5ooJ/tHJEau2VQF1qEB3LflJWUu5vYL6UVZTDjVghvA6fdZbtGpMby/X14rkc0HXftIu2n+2zniIiISCNx2GGRMWYkgOM4c4BcY8zAA99T9dr+LgGiHMeZVHWMUVXPX+w4Tj/HcfRTtsgh7Mgr5tlv1nBG11jOTWpuO0fkiAQH+PLQ0B6k7dzLez9ttp1Tu359BbJXw+CnK++CJtKIfNk6lMXRgbT8fjxF+em2c0RERKQRqO7KouOAjVVfbwT6VndAx3HecBznjaqHCcC+YVKEMSbhqCpFvMQjM1ZR4XEYMzwJY4ztHJEjdk6PeM5KjOO5OWvZnltsO6d27NkC85+ExCHQ9TzbNSJHzhge7xlHUIWbDV9cYbtGREREGoHqhkUH7qwbXdMDVw2GchzH2TdsigJyjDHjD/H+UcaYxcaYxdnZ2TU9jUiTMS8ti5kpO7nxrM60iWpmO0fkqBhjGD2sBx7H4eHpqbZzjp3jwMw7wLjgPK2ilsZrc6g/73eKJHl9CltXf2I7R0RERBq46oZFuVQOeY7GSMdxrt33oOqKo1wql7ONPPDNVa/3dxynf2xs7FGeUqRxKi5z8+AXK+kUF8I1p+gCPGnc2kQ148azOjMrNZO5qzNt5xyb1dNh3Sw4414Ib227RuSYvNMlkq3N/DAzb8NT3kSu/BMREZE6Ud2waBH/vbooAZh9mPf+zhgz0nGcp6q+Hlh11dC+AdHuoyoVacJembeejJxiHhmehL+vblIojd8/Tk6gc1wID05LpbjMbTvn6JTuha/ugvhkOOE62zUix6zUx8UTPWNotbeQ1XOut50jIiIiDdhhfyut2qQ6Yd/G1vs2sz7g7mcjgf77hkFV732y6s5nS6reNpH9Nsjet/m1iMD6rL2M/34DF/ZtxYCONV7pKdKg+fu6GHtBEttyi3nx23W2c47OvMdh7w4Y8hz4+NquEakVv8QF803LEDotmkpe5lLbOSIiItJAVfvT774rhA54btB+X08CJu33eA7Q8SCHmnPAv0W8nuM43DdlJc38fbl3cDfbOSK16oSEaEb2a82b329kRJ9WdIkPtZ1UcztWwILXoN9foc1xtmtEatW4pBhOzCoic9pVhF+TArqhgoiIiBxA611ELJr82zYWbMrhrnMTiQkJsJ0jUuvuOS+RkEBf7p+yEsdxbOfUjMcNM26GZtEw8CHbNSK1blegL690i6LL9gw2LR5nO0dEREQaIA2LRCzJLSrjsZmr6dM2gsuOa2M7R6RORIcEcM95iSzcnMOkJVtt59TMkndh2xI45zEIirRdI1InJrUPZ1V4AOFzn6C8SNtJioiIyP/SsEjEkie/XkNucTmPXpCMy6UlANJ0XdyvDf3aRfLYzNXsKSyznXN4ezNhzhjocCokX2y7RqTOeIzh0V6xhJeUs/bLq2zniIiISAOjYZGIBUu27OGThen87cT2dG8ZZjtHpE65XIZHRySRX1LBE1+l2c45vG/ug4piOP9Z7eMiTV5aRCCfdQinW+pPZG/+xnaOiIiINCAaFonUswq3h/umpNAiPJCbB3WxnSNSLxKbh/GPkzswYXEGizfn2M45uA3zIOUzOPkWiOlsu0akXryWGMXuAB+Kpo3CcVfYzhEREZEGQsMikXr23s+bSdu5l4eG9iAkQLfjFu9x08DOtIoI4r4pKyl3e2zn/K/yEvjyNohKgJNvtV0jUm8K/HwYlxRDuz17WPf9XbZzREREpIHQsEikHm3PLebZ2Ws5MzGOc3rE284RqVfN/H15aGh31mTu5Z0fN9nO+V8/Pgc5G+D8ceAXaLtGpF7NbhnCT3HNaPXTOxTv2WA7R0RERBoADYtE6tHD01PxOA4PD+uB0X4o4oXO7tGcgd3ieX7OOrbuKbKdU2nXevjxWUgaCR3PtF0jUv+M4ankWHw9DlumXWG7RkRERBoADYtE6smcVZnMSs3khjM70yaqme0cEWtGD+te+e8vUnEcx26M48CXt4JvEJzzmN0WEYu2BvvxVpdIEjensXXlu7ZzRERExDINi0TqQWFpBQ99kUqX+BBGnZpgO0fEqtaRzbhlUGfmrM5iVmqm3ZiUSbDpOzjrAQjV0lDxbh92jGRTiB9+X92Dp6zQdo6IiIhYpGGRSD14fs5atuUW89iIZPx89G0n8reTOtCtRRijv0iloNTSHZiK98Cse6BlX+h/tZ0GkQak3MfweM9Y4guLSZv1D9s5IiIiYpF+axWpY6nb83jnp81cfnwb+rePsp0j0iD4+bh4bEQSmXtLGPfNGjsRc8dA0W4Y8hy4fOw0iDQwS2KaMaN1KJ1/+4rcHQts54iIiIglGhaJ1CG3x+HeKSuJbObHXecm2s4RaVD6tI3kyhPa8f7Pm0nZmle/J89YBIvfhROug5a96/fcIg3ccz1iKPI17J7y58p9vURERMTraFgkUoc+WrCF5Rm5PDCkOxHN/G3niDQ4d5zbleiQAO6ZsoIKt6d+TuqugBm3QGgLOOPe+jmnSCOSG+DDi92j6Zi1kw2/jrWdIyIiIhZoWCRSRzLzS3j66zWc3CmGYb1a2s4RaZDCAv14aGh3Vm7L54NfttTPSReOh8wUOO8JCAitn3OKNDLT2oaxLDKQ6HnPU1qww3aOiIiI1DMNi0TqyJjpqyh1exh7QRLGGNs5Ig3W+cktOL1rLOO+WcOOvOK6PVneVvj2Ueh8NnQbVrfnEmnEHGN4vFcsIeUVrJ/+J9s5IiIiUs80LBKpA/PSsvgyZQc3nNGJ9jHBtnNEGjRjDI8MT8LtOIz+IrVuT/bVXeB4YPDToCGuyGGtDwvgo4QIeqxZwvZ1n9vOERERkXqkYZFILSsqq+D+qSvpFBfCqNMSbOeINAptoppx01ldmJWayexVmXVzktXTIW0GnH43RLavm3OINDFvdI1iWzNfnOk34pSX2M4RERGReqJhkUgte2HuOrblFvPoBUkE+Op23CI19Y9TOtA1PpSHpq2ksLSidg9ekgcz74D4ZBjwr9o9tkgTVuLr4vGesbTKL2DN7Ots54iIiEg90bBIpBal7czn7R82cUn/1pyQEG07R6RR8fNx8diFSWzPK+G52Wtr9+Bzx8DenTDsBfDxq91jizRxv8QF81WrEBIWTyVv5yLbOSIiIlIPNCwSqSUej8M9k1MIC/LjnvO62c4RaZT6tYvi8uPb8u7Pm1m5La92Dpq+ABa9DSdcB6361c4xRbzMuKQYin0MuydfBR6P7RwRERGpYxoWidSSjxemszQ9l/sGdyMy2N92jkijdfe5iUQ28+O+KSm4Pc6xHayiDKbfBGGt4Mz7aidQxAvtCfDluR4xJGTtYNMvY2zniIiISB3TsEikFmTtLeHJr9MYkBDNhX1b2c4RadTCm/nxwJDuLN+ax0cLthzbwX5+EbJXw/nPQEBo7QSKeKnpbUJZHB1E7PwXKc1Lt50jIiIidajaYZExZqQxZqAx5s5DvD7QGDO7us9UdxyRxuyRGaspLfcwdkQSRrfjFjlmw3q15JTOMTz19Roy84/yDky7N8B3T0H3C6DrebUbKOKNjOHRXrH4uT2kT7vcdo2IiIjUocMOi4wxIwEcx5kD5BpjBh74nqrXDvuZmhxHpLGatyaL6cu3c/3pHekYG2I7R6RJMMYw9oIkyt0eHpqWeuQHcJzK5We+gXDek7UfKOKl0kP8ebtLJJ03rmRnynu2c0RERKSOVHdl0XHAxqqvNwJ9a3DMg33maI4j0uAVlFZw3+QUOsWF8M8zOtrOEWlS2kUHc9PAznydupOvV+44sg8v+xg2/wCDRkNo8zrpE/FW73eKZEOoPz5f3YWnNN92joiIiNSB6oZFEQc8rsm9wA/2mWqPY4wZZYxZbIxZnJ2dXYPTiNj39Ndp7Mgv4cmLkgnw9bGdI9LkXHNKAt1bhPHAtFTyispr9qGCbPjmPmjzf9D3r3XaJ+KNKlyGsb1iiS0qYd3Mv9nOERERkTpQ3bAoF4g6wmMe7DPVHsdxnDccx+nvOE7/2NjYIzylSP1bsiWHD37dwl8GtKdfuyP9NhGRmvDzcfHUyJ7kFJbx2MzVNfvQrHuhtACGvgAu3cdBpC6siAris/ZhdFo+hz1bvrWdIyIiIrWsup+iF/Hfq4ISgNmHee/hPnM0xxFpsEor3Nz1eQotw4O445yutnNEmrSkVuFcc0oCExZn8NP6XYd/8/q5kDIRTrkV4hLrJ1DES73cLZqcAB8Kpl4N7grbOSIiIlKLDjsschxnEpCwb0PqfZtZ73/3s6rNq/vvt4n1Hz5zqOOINFavfLue9VkFPDoiieAAX9s5Ik3ezQM70yEmmHsmp1Bc5j74m8qKYMYtEN0ZTr61fgNFvFCBnw9PJsfSZs8e1s3T95yIiEhTUu31+Y7jPFU18Hljv+cG7ff1JMdxIqsGQof7zB+eE2mMVu/I59X5GxjRpxWnd42znSPiFQL9fHj8wmTSc4p4dvaag7/puycgdwsMfR78Aus3UMRLzWsRzPzmwbT55QMKso/izoUiIiLSIGkzB5Ej4PY43P35CsKC/HhgSHfbOSJe5f8Sorn8+La8/eMmlmfk/u+LO1bAzy9D3z9D+5PtBIp4I2N4MjkWN4YdUy4Hx7FdJCIiIrVAwyKRI/DuT5tYvjWP0cN6EBXsbztHxOvcMziR2NAA7vp8BeVuT+WT7gr44gZoFgWDxtgNFPFCWUG+vNw9is7bt7Bp4RO2c0RERKQWaFgkUkPpu4t45ps1nJUYx9CeLWzniHilsEA/xl6QTNrOvYz/bkPlkz+/ADuWweBnICjSbqCIl5rUPpxlkYHEzHmakrwttnNERETkGGlYJFIDjuNw75QUfF0uxo5IwhhjO0nEaw3qHs/5PVvw4tz1bElbAvOfgO7DoccFttNEvJbHGMb0icPf7WHr5xdrOZqIiEgjp2GRSA18tmQrP67fxV3nJdIiPMh2jojXGz20ByF+UDbpehz/EBg8znaSiNfbEuLPa4lRdEpfw7YlL9rOERERkWOgYZFINbL2ljB2xiqObx/Fn45vaztHRIDY0ADe67aIzhVr+KHznRASaztJRICPOkaQEhlA6DdjKN+7zXaOiIiIHCUNi0SqMfqLVEoqPDx+UTIul5afiTQI2WtJXvsyi4NO5Ppl7dmWW2y7SESoXI72cO94AivcpE++1HaOiIiIHCUNi0QOY1bqTmam7OSmszrTMTbEdo6IAHjcMO1fGL8gWlzxGg6G+6ek4GiPFJEGYVOoP+O7RtFxUwo7l75uO0dERESOgoZFIoeQV1zOA1NX0r1FGKNOTbCdIyL7LHgdti6E856iVZv23H52V+atyeaL5dttl4lIlQ87RpAaEUDQ1/dTUbDTdo6IiIgcIQ2LRA7hkRmr2FVQypMX9cTPR98qIg3C7g0w9xHoci70vASAv5zYnj5tI3joi1Sy9pZYDhQRALfL8HDvOJqVVZA+9TLbOSIiInKE9BuwyEHMXpXJpCVb+efpnUhuHW47R0QAPB6Y9m/w8Ychz4Gp3EPMx2V4emQvisvc3PO5lqOJNBQbwgJ4q0skCeuXkrn8bds5IiIicgQ0LBI5QE5hGfdMTqFbizBuPKuz7RwR2WfRm5D+M5z7OIS1/J+XOsWFcOe5icxNy+KzJVstBYrIgd7rHMmasAACvrobd2G27RwRERGpIQ2LRPbjOA73T00hr7iMZy/phb+vvkVEGoScTTBnNHQaBL2vOOhb/nZie07oEMWY6avYuqeofvtE5KAqXIaH+sQRUlrGZi1HExERaTT0m7DIfr5Yvp2ZKTu5ZVAXurUIs50jIlC5/OyLG8D4wNDnf19+diCXy/DMxb1wHIc7J63A49FyNJGGYF14AO90jqTjusVkprxnO0dERERqQMMikSqZ+SU8OC2VPm0jGHWK7n4m0mAseQc2/wDnPArhrQ/71jZRzbh/SHd+3rCbD3/dUk+BIlKdt7tEsS7UH78v78RdtNt2joiIiFRDwyIRKpef3fX5Ckor3Iy7uBe+uvuZSMOQmw6zH4KEM6Dvn2v0kcuOa8PpXWN5/KvVbMwuqONAEamJCpdhdJ84wkpL2aDlaCIiIg2efiMWASYsymD+mmzuPjeRhNgQ2zkiAv9dfgYw7MVDLj87kDGGJy/qSYCvD7d9thy3lqOJNAhpEYG83ymSLmsXsmPl+7ZzRERE5DA0LBKvl5FTxCMzVnFix2j+PKC97RwR2WfhG7BxPgwaAxFtj+ij8WGBjBneg6Xpubzx/ca66RORI/ZmlyjWh/oTOON2ygt22M4RERGRQ9CwSLyax+Nw+2fLMcbw1MieuFw1u3JBROpY5iqY/SB0ORf6X31UhxjWqyWDk5vz3Oy1pO3Mr+VAETka5T6G+/rGE1xWTsZnI8DRlX8iIiINkYZF4tXe+3kzCzbl8ODQ7rSObGY7R0QAKkph8jUQGAbDXq7x8rMDGWN4ZHgSYUG+3DphOWUVnloOFZGjsT48gJe7RZGwZTXbf3ncdo6IiIgchIZF4rXWZxXw5NdpnJUYx8X9Dn+HJRGpR3PHQOZKGP4KhMQe06GiQwJ4bEQyq3bk89K362opUESO1ccJESyICSJq7tOUZKfazhEREZEDaFgkXqnC7eG2z5YT5O/D4xcmY47yygURqWUb58MvL0P/v0OXc2rlkGf3aM5FfVvz6vwNLMvIrZVjisixcYxhdJ94ylyG3RMuBHe57SQRERHZj4ZF4pVe/24DyzNyGXtBEnFhgbZzRASgKAemXA8xXeDssbV66AeHdicuNIDbJi6jpNxdq8cWkaOTFeTL2F6xtNq1k63f3GA7R0RERPZT7bDIGDPSGDPQGHNnTV43xvQ1xmwwxiyp+ufJquf37P9YxJbU7Xm8MHcdQ3q2YEjPlrZzRAQqN7mdcTMUZsGFb4J/7e4hFh7kx1Mje7Ihu5CnZ62p1WOLyNGb2zKE6W1CabHgE/Zumm07R0RERKocdlhkjBkJ4DjOHCDXGDOwBq9HOY7T0XGcfsA1wPiqt1/sOE4/x3Huqu0/hEhNFZe5ufnTZUQ08+eR4Um2c0Rkn+WfwKppcMZ90LJ3nZzilM6xXPV/7Xj7x018vza7Ts4hIkfu6aRYdjbzo2zSX3FK8mzniIiICNVfWXQcsLHq641A3+perxoc7ZPgOM6+1yOMMQnHEityrMbMSGV9dgHPXdKbyGB/2zkiApCzCWbeAe1OgpNuqtNT3Tu4G53jQrh14jKy9pbU6blEpGYK/Vw80CeOiMICMqZcbjtHREREqH5YFHHA4+iavm6MGeU4zqT9XosCcowx4zkIY8woY8xiY8zi7Gz9ja/UvunLt/PJwgyuP60jJ3eOsZ0jIgDuCphyLRgfGDEeXD51erogfx9evqIve0squG3icjwep07PJyI1szw6iHe6RNJ2zU/sWvam7RwRERGvV92wKJfKIc/RvD5o/weO47zhOE4ulcvVRh745qrX+zuO0z829thulSxyoIycIu6dnEKfthHcMqiL7RwR2efHZyFjAZw/DiLa1MspuzYP5cGh3flh3S7e+GFj9R8QkXrxVpcoVkYEEDjzbsrzttjOERER8WrVDYsW8d+rhxKAA3cePOjrxpj/ueKo6qqhfQOi3UddK3IUyt0e/v3JUjDw4mV98PPRTQBFGoSti2H+E5B8MfS8uF5PfcXxbRmc3JxnZq3ht/Q99XpuETm4Cpfh/r7xuNwedkwYDh6P7SQRERGvddjfmquWkSXs29h6335ExpjZh3udqiVn+x1qIvttkH3A8jSROvXMN2tYnpHLkxf1pE1U7d5hSUSOUmkBTL4GwlrC4Gfq/fTGGB6/sCfxYYHc+MlS8orL671BRP4oI8SfcUnRtN2+iYzv7radIyIi4rWqvcTCcZynHMeZ4zjOG/s9N6ia1zc6jnPtfo9zq94zx3Gcp2rzDyByON+tzWb8dxv50wltGZzcwnaOiOwz657Kja1HvA5BB25/Vz/Cg/x46Yo+7Mgr4d7JKTiO9i8SaQimtg1jfvNg4n94g/xtP9vOERER8UpajyNNVlZ+CbdOWEbX+FAeGNLddo6I7LNyMvz2AZx8M7Q/2WpK37aR3H52V75M2cEnCzOstohIFWN4pFcc+X4uCidcilO613aRiIiI19GwSJokj8fhlonLKCyr4OUr+hDoV7d3WBKRGtq1Dr64AVofD6ffa7sGgGtPTeCUzjE8PD2VNTv1S6lIQ5Ab4MP9feOJy89ny2fDQVf+iYiI1CsNi6RJeu27Dfy0fjcPD+tB5/hQ2zkiAlBWCBOuAt8AuPg98PW3XQSAy2V49pLehAb68e+Pf6O4zG07SUSARbHNeD0xivbrl7Dz57G2c0RERLyKhkXS5CzZsodnZ69lSM8WXNK/fm7FLSLVcByYcStkp8FFb0F4K9tF/yM2NIBnL+nFuqwCxsxYZTtHRKq82zmSH+OaET1nHEXpP9jOERER8RoaFkmTkldUzo2fLKVlRCCPXZiMMcZ2kogALHkPVnwKp98DHc+0XXNQp3aJ5brTOvLJwnRmrNhuO0dEAMcYHugbz65AX0omXIpTuNt2koiIiFfQsEiaDMdxuHvyCjLzS3jp8r6EBfrZThIRgO1L4as7oeNZcOodtmsO67azu9C7TQT3fJ5CRk6R7RwRAfL9fbizfzwhxUXsmDAUPB7bSSIiIk2ehkXSZHy0IJ2vVu7kznO70ruNnVtxi8gBivfAxL9AcBxc+Ca4GvZ/dvx8XLx0eR8w8O9PllJWoV9KRRqCVZGBjOsRQ8v0VLK+vdt2joiISJPXsH9qF6mhpel7GDN9Fad1ieUfJyfYzhERqPzb/ynXQ/72yg2tg6NtF9VIm6hmPHlRT5Zn5PLol9q/SKShmNQ+jK9ahRD943gK1820nSMiItKkaVj0/+3dd5wV1f3/8de5bXtnGyy9S4elCcaGStSvxohiA6Mm2GLUmPpN8kuipvj9Jt8UEwu2qCiimNgThViioMAuCtKk97psr7ed3x/37rIgwoIsc3f3/Xw87mNmzsy9+yYPJzP3c8+cI23e3qp6bppVTE5qHH+cOhyXS+MUicSEhX+Ctf+E834FXUc7neaYnD8kn29O7MmTH27h+aJtTscREQBj+NWwHLYm+wjN/Qbhiu1OJxIREWm3VCySNs0fDHPzrKVU1gWZOa2QjKTYmIpbpMPb9D78+24YdAmMmeF0muPyo68OYEKfLH76jxV8vLXM6TgiAtR5XHxvdB6eYIA9sy+AUMDpSCIiIu2SikXSpv3i1ZUUbynjfy8byimdU52OIyIAVbth7vWQ2Rsuuh/a6KyEHreLv1w5kty0OG6aVczeqnqnI4kIsDnFxz3Ds8nfvZmdb9zodBwREZF2ScUiabOeWbSFZxdt5eYzenPh0M5OxxERgFAwUijyV8PUpyEuxelEX0pGko+Z0wqprAty86ylGvBaJEa81SWFOT3S6Fz8ImXLn3Q6joiISLujYpG0SUWbS/nFKys5vV823zu3v9NxRKTR2/fAlgVw4R8gZ6DTaU6Igfmp/O6yYRRvKeMXr650Oo6IRP1hUCdWpMfje+VOGvZpMHoREZETScUiaXN2V9Rz06yldElP4M9XjMCtAa1FYsPqV2HBH2HUdTDsCqfTnFAXDM3nljN68+yirTyzaIvTcUQECLgNPyzMJWhg/7MXYhuqnI4kIiLSbqhYJG1KfSDEjbOKqfMHmTm9kLREr9ORRARg5yfw9xnQZRRM/q3TaVrFXef254z+2fzilZUUbS51Oo6IALsTvfxkVA65ZfvZPvurEA45HUlERKRdULFI2gxrLT99aQXLtpXz+8uH0y+3bdYLkjIAACAASURBVI+FItJuVO6E2VdAYhZcMRu88U4nahVul+FPV4ygICORm2YtZXeFBrwWiQUf5iTxuyGd6Lr5U3a93jZnXxQREYk1KhZJm/HUh1uYW7yd75zdl8mD85yOIyIADdXw7FRoqIIrn4OUXKcTtaq0BC8zp42izh/kxlnF1AfUi0EkFjzfM53neqaRXzyX0o/+z+k4IiIibZ6KRdImfLhhP3e/topJA3O44+y+TscREYg87vH3GbBnBUx5AvIGO53opOibm8L/TR3Osm3l/PSlFVhrnY4kIsD/DerEgpxE0t78JXXr3nA6joiISJumYpHEvB3lddz67FJ6ZCXyh6nDcWlAa5HYMP/n8NnrkTGK+p3rdJqT6rxBedx+dl/mFm/nqQ814LVILAi5DD8elcem5Djs89MJ7dUMaSIiIsdLxSKJabX+IDc+XUQgGGbm9EJS4jWgtUhMKP4bLLwfRn8Lxt7odBpH3H52XyYNzOXu11axcEOJ03FEBKjxurh9bB51Lkvl01+FGp2bIiIix0PFIolZgVCYW59ZyqqdlfzpyuH0zk52OpKIAGx8F16/C/pMarczn7WEy2X4w9Rh9OqUxI1PF7Nmd6XTkUSEyAxp3x2TR2JNBftmnQfBBqcjiYiItDkqFklMstby33//lHc+28c9XxvMWQPa96C5Im3GvrUwZzpk9YUpj4Pb43QiR6XEe/nb9WNI8nm49vHF7CivczqSiAArMuL5+YgcsnetZ9/cK0Bji4mIiBwTFYskJv3+rbW8ULyd28/uy9VjuzsdR0QAavbDs5eBxwdXzYH4NKcTxYQu6Qk8ef0Yav0hpj+2iLIav9ORRASY1yWFBwZkkr3mbfb/+0dOxxEREWlTjlosMsZMMcZMMsb8oKX7jTFlxphiY8x9Lf0ckUZPfbiZv7yznivHdOWOSZr5TCQmBBtgztVQuQuumA0ZKuI21z8vhUenF7KtrI4bnlxCnT/kdCQRAR7rm8FrBSlkffAQFR8/7nQcERGRNuOIxSJjzBQAa+18oNwYM6mF+y+z1o6y1v6wJZ8j0uiNT3fx81dWMmlgLvdcPBhjNPOZiOOshVdug60fwiUPQtfRTieKSWN7ZfHnK4bz8bZybpv9McFQ2OlIImIM9w7L4ePMBBJevYvaLe86nUhERKRNOFrPotHAxuj6RmBkC/enG2N6HcPniPDRxv3c8dwnjOyWwf1XjsDj1lOSIjHhvftg+Rw48ycw+FKn08S0yYPzufviwcxfvYefvbwCq3FSRBwXcBu+NzqPvQlugs9eTqBkrdORREREYt7Rvo2nH7Kd1cL9mUCpMebhFn4OxpgZxpgiY0zRvn37jhJL2ps1uyv51lNFdMtK5LFrC0nwuZ2OJCIAHz4A7/4Ghl0FX/m+02nahGnjunPbWX2YvXgbf5y/zuk4IgKUx7m5fUw+YRuk6okzCZdvcTqSiIhITDtasaicSOHnmPZba2daa8uJPHI2pQWf0/ieQmttYXZ29lFiSXuyo7yOax9fTKLPzZPXjyE90ed0JBEBKHoC3vwxDLwILrof9Fhoi333nH5cXljAn/69jmcW6UupSCzYnOLj1nH5+BpqKX/8dGzVbqcjiYiIxKyjFYuWcKBXUC9g3tH2R3sITYm27W/h50gHVVbjZ/pji6j1h3jy+jF0SU9wOpKIACybA6/dCX3OgUsfA7fH6URtijGGX18yhLMH5PCzl1bw5kp9KRWJBWvS47ltXD4JNeWUPXE61JY6HUlERCQmHbFYZK2dC/RqHJA6OkA1xph5R9j/PM0GsbbWzv2iz5GOrc4f4oYnl7CtrI5HphcyIC/V6UgiArDqFXjpZugxEaY+DR719jseHreLv1w1kmFd0/nO7I9ZsllfSkViwfLMBO4ck09S+R5KnzgD6iucjiQiIhJzTCwOvllYWGiLioqcjiGtKBgKc9Ospfx7zR4euGokXx2S73QkEQFYNw9mXwmdR8C0f0BcstOJ2rzSGj9THlpISVUDc28+lX65KU5HahUfV3/MHRvuoDpU7XQUkRaZuKeG3y/eRVVefzKuewd8SU5HEhERaXXGmGJrbeHRjtN0U3LSBUNh7nphGfNX7+HuiwapUCQSKza9D3OugZwBcPULKhSdIJlJPp68bgzxXjfXPLqIDftUTBGJBR/kJvGTUXmk7vqMsqe/CoF6pyOJiIjEDBWL5KQKhMLcPucTXv5kJz+Y3J9p43s4HUlEALYtgWenQkYPmPYSJBw6iaV8GV0zE3nmm2MJW5j68Ees21PldCQRAeZ3Tubu4TlkbFtG6bMXQdDvdCQREZGYoGKRnDT+YJjbnv2Y15fv4ifnD+SWM/o4HUlEAHYtg1mXQnJOpFCU1MnpRO1S39wUnpsxDpeBK2Z+xJrdlU5HEhHgtW6p/GZINpmbFlH6/BQIh5yOJCIi4jgVi+SkaAiGuOWZpfxr5W7+34Wn8K2v9HI6kogA7F0DT18CcSlw7SuQqsdCW1OfnGTm3Dger9vFlTM/YuVODawrEgvm9kzjj6dkkbn2Pfa/eCWEw05HEhERcZSKRdLq6gMhbnq6mPmr93DPxYO4fmJPpyOJCEDpRnjqYjDuSKEovZvTiTqEnp2SmHPjOBJ9Hq56ZBGfblfBSCQWPN0ng4f6Z5K18k32vXIdxOAkMCIiIieLikXSquoDIb71VBHvfLaPX18yRGMUicSKknXw5EUQ8sP0lyGrt9OJOpTuWUk8N2McKfEernr0Iz7eWuZ0JBEBHumXwVO908n+5CX2vnydehiJiEiHpWKRtJo6f4gbnlzCB+tL+J8pQ7lqrHotiMSEHUvh8fMgUAfTX4LcU5xO1CF1zUxkzo3jyUzyMe2xxRRvKXU6kogYw59OyWJWr3RyPvkH++d8XYNei4hIh6RikbSKmoYg33hiMR9u2M/vLxvG5YVdnY4kIgAb3oEn/wt8SXDDW5A/zOlEHVqX9ATmzBhPdkoc0x9bzOJNKhiJOM4Y/jAoiz8PzCLrs3coe/o88Nc4nUpEROSkUrFITrjqaKGoaEsZf5g6nK+PLHA6kogArPwHPHt5ZGyi69/So2cxIi8tnjkzxpGXFs+1jy9m4YYSpyOJiDE82TeDu4flkLplKRWPnw61KuaKiEjHoWKRnFCV9QGmPbaIj7eW8+crRnDx8C5ORxIRgCWPwgvXQeeRcN0bmvUsxuSkxvPcjPF0zUzg+r8t4YN1KhiJxIKXu6fyg9F5xO9dT+UjE6Biu9ORRERETgoVi+SE2Vlex9SHP2LFjgr+ctVILhiqL6MijrMW3r0PXr8L+p4L0/4BCRlOp5LDyE6JY/a3xtEjK4nr/7aElz/Z4XQkEQHezU/m2+M646raTfUjE2DfWqcjiYiItDoVi+SE+HR7BV/76wK2ldby6LWjmTw4z+lIIhIOwz9/AO/+GoZdCVc8A75Ep1PJEWQlx/HcjHEM75bO7c99wh/nr8Vq+m4Rxy3tlMC3JnShIVBN7aNfIbx9idORREREWpWKRfKl/WvFbi57eCFet4sXbz6V0/tlOx1JRIJ++Ps3YfFMGP9tuPgBcHudTiUtkJ7o4+kbxnDpyAL+OH8dd875hPpAyOlYIh3e2rQ4rp/YhTJ3kMDfJhNc95bTkURERFqNikVy3Ky1PPTeBm5+ppgBeam8dOsE+uelOB1LRBqqYfZUWPEinHM3nPcrcOn/7tuSOI+b3102lO+f15+XPtnJNY8uYn91g9OxRDq87Ulerp/Yha2JHph9OXXLn3E6koiISKvQtwc5Lv5gmB+9+Cm//ecazh+Sz3MzxpGdEud0LBGp2gNPXQQb34WL/woTbnc6kRwnYwy3ntmHv1w1gk93VHDJAwtZv7fa6VgiHV5JvIdvTshneUYCcX+/hYoPfhsZH05ERKQdUbFIjllFbYBrH1/MnKJt3HZWH+6/YgTxXrfTsURk22KYeTrsWQVTZ8GIa5xOJCfAhUM789yMcdT6Q1zywAIWrNdMaSJOq/a6+fa4PN7LSyZt/m8oe+EK8Nc6HUtEROSEUbFIjsnmkhoueXABRVtK+f1lw7jr3P64XMbpWCIdm7Ww+BF44nzwxMM358OAC5xOJSfQiG4ZvHTrqXROS+Daxxcze/FWpyOJdHgNbhffH53Lg/0zSVv1LypnjoPSTU7HEhEROSFULJIWW7yplEseWEBpjZ9ZN4zl0lEFTkcSkUAdvHQzvPE96H0WzHgH8gY7nUpaQUFGInNvHs+EPp348d8/5TdvrCYc1qMvIk6yxvBo/0xuH5sPFduof3g84bVvOh1LRETkS1OxSFrkxeLtXPPoIjISfbx0ywTG9spyOpKIlG2Gx86FZc/BGf8NVz4HCRlOp5JWlBLv5bFrC5k+vjsP/2cjN80qproh6HQskQ5vYW4S13ylK9viLDx7OQ3v3gvhsNOxREREjpuKRXJENQ1BvvfCMu56YRmjumfw91tOpUenJKdjicj6+TDzDCjfAlfNgTN+qBnPOgiP28XdFw/mF/91CvNX7+HCP7/P8u3lTscS6fB2JHn5xsTOvFmQSty7/0vNsxdDnc5NERFpm/TNQr7Qih0VXHj/B7y4dDvfOasPT98whvREn9OxRDq2cBj+878wawqkdoEZ70K/85xOJQ74xoSePDdjPP5gmEsfXMjM/2zQY2kiDqv3uPjpiGzuG9KJuA3/oeahsZFJB0RERNoYFYvkc8Jhy6Pvb+SSBxZQ5w/x7DfH8d1z++Nx6z8XEUfVV8Cca+Dte2HIFLhhHmT2cjqVOGhMz0zeuP00zh6Qy6/fWMO1Tyxmb1W907FEOjZjeL5nOjNO7UJdfQn+R04j8Okcp1OJiIgcE337l4OUVDdw/ZNLuPf11ZzRP4d/3n4a43trfCIRx+1aDjPPhHVvwuT74OuPgC/R6VQSA9ITfTx4zUh+dclgFm8q5fw/vc87n+11OpZIh7csK4GrTy9gVaoP74szqHztVgiomCsiIm3DUYtFxpgpxphJxpgftGS/MSY92jbFGHNfs+PKjDHFzdsktvxn7T4m//F9Fm7Yzz0XD2LmtFFkJOmxMxFHBf3w7m/hkTPBXw3XvgrjbgJjnE4mMcQYw9Vju/PqbRPplBzHdU8s4d7XVtEQDDkdTaRDK4n3cOOp+czumU5q0SyqHhiB3V7kdCwREZGjOmKxyBgzBcBaOx8oN8ZMasH+y4FMa+3c6DEzoodfZq0dZa394Qn+N8iX5A+G+c0bq5n++GIyk7y88u0JTBvfA6MvoyLO2rUcHjkL3v0NDL4UbvkIup/qdCqJYf1yU3jp1glMH9+dRz/YxKUPLmTjvmqnY4l0aEGX4XdDOnHruM7U1O/DPjaJ+rd+pF5GIiIS047Ws2g0sDG6vhEYebT91tqZ1tqZ0bZewPzoeroxRoNrxJjNJTVMeWghD/9nI1eP7cbLt05kQF6q07FEOragH975TaQ3Uc1euGI2fH0mJGY6nUzagHivm7svHszMaaPYXlbHhfd/wAtF27BWg1+LOOmjnESmnlHAq93SiF/4ILUPjgb1MhIRkRh1tGJR+iHbhw5e84X7o4WhUmttYzEpEyg1xjx8uD9kjJlhjCkyxhTt27fvKLHkywqGwjz6/kYu+PP7bNlfy0PXjORXlwwhwed2OppIx9bYm+i93x7oTTTgfKdTSRt07qA8/nn7aQwtSOP7c5cz4+lidpTXOR1LpEOr9rq5e1ikl1Fl3S7Cj00i8OZ/q5eRiIjEnKMVi8qJFHmOZ/8Ua+2NjRvRHkflRB5Xm3LowdH9hdbawuzs7KPlli+haHMpF97/Afe+vrppJp3Jg/OdjiXSsak3kbSC/LQEnvnmOH701QF8sK6ESb9/jwff3YA/GHY6mkiH1ryXkffDv1KnXkYiIhJjPEfZv4QDvYd6AfNast8YM8Va+z/R9UnRfaXRcYz2n4DcchxKa/z89p+reb5oO53T4nnomlGcNyhXYxOJOG3XcnjpFtjzKQydCpN/qyKRnDBul+Gm03tz4dB87n51Fff9aw0vLt3OPRcP1myXIg5q7GX0Vn4iP1u2i7jHJuEfdyPxZ/0SvPFOxxMRkQ7uiD2LosWdXo0DW0cHssYYM++L9kfX74vOfFYc/ajnaTZAduPg13JyhMOW2Yu3ctbv3+XvS3dw4+m9mPfd05k8OE+FIhEn1VfC/F+qN5GcFAUZicycXshj1xZSHwhx5SMfceecT9hX1eB0NJEO7aCxjD58KDJj2vq3nY4lIiIdnInFAS8LCwttUZG64p4IK3ZU8NOXVvDJtnLG9Mzk3q8Npl9uitOxRDq2UBCWPhmZ5axmHwy7Es77tYpEctLU+UM88O56HnpvA/FeN98/rz9Xj+2O23X8PyB8XP0xd2y4g+qQZl8TOV7j9tbyk+X76FwboLbnqSRO/j3knuJ0LBERaUeMMcXW2sKjHqdiUftUWR/g/95ay1MfbiYzycd/nz+QS0Z0UU8iESdZC2vfhHk/g5K10H0CnHsPdBnldDLpoDbsq+b/vbyCBev3M6RLGvd+bTDDuh46d0XLqFgkcmJ4Q5apmyu4YW0pyUFLcPiV+M76OaTkOR1NRETaARWLOih/MMzc4u38Yf5aSqobuGZsd753bn/SEr1ORxPp2HYtgzd/Apvfh6w+cM7d0P98UAFXHGat5bXlu7jntVXsq27g8lFdue3sPhRkJB7T56hYJHJipflDzFhbwaWbysDtwzXxTtynfgd8SU5HExGRNkzFog4mEArzYvF27n97PTvK6xjZLZ1fXDSIoQXH9wuxiJwgFdvh7Xth2XORx8zO+DGM+ga4VcCV2FJVH+AP89Yx66MtWCyXF3bl1jP70Dk9oUXvV7FIpHUUVPu5fU05Z+2spCEpE9/Zv8QMvxpcbqejiYhIG6RiUQcRCIX5x9Id3P/OOraV1jGsazp3TurL6f2y9ciZiJPqK2HBH+HDv0YePxt3M5z2XYhPczqZyBHtLK/jr++s5/mibRgMU0d35ZYze5OfduSikYpFIq1raGkdd60sZXBZHXXZvUmY/DvofZbTsUREpI1RsaidC4bCvPTJTu5/ex1b9tcytCCNOyb15cz+OSoSiTipeh8seQQWPwJ1pTDkcjj7Z5DezelkIsdke1ktf31nAy8UbcNlDFeN7cbNZ/QmN/XwU3qrWCRyEljLOTuruW11KV1qA9QUDCPptB9D3/PAdcRJjkVERAAVi9qtYCjMK8t2cv/b69lUUsOgzqncOakfZw9UkUjEUfs3wML7YdlsCNZHxiP6yvc0eLW0edtKa/nrO+uZW7wdtytaNDq9NzmHFI1ULBI5ebwhy6VbKpi2oYK8ugD1md2Jn/i9yA8U3sMXdEVEREDFonanzh/i1WU7eei9DWwsqWFgfip3TurLOafkqkgk4qRti2HBn2DN6+D2wbAr4NTboFNfp5OJnFBb99fyl3fW8eLSHXiiRaNrx/egR6fIYLsqFomcfJ6wZdLOaq7dUEG/inr8iRl4x30bM/oGSMhwOp6IiMQgFYvaiQ37qnnmo63MLd5GZX2QAXkp3DGpL+eekofLpSKRiCPCYfjsDVj4Z9i2COLTYcy3YMwMSM5xOp1Iq9pcUsP9b6/n5U92EAxbTuvbiWnjupPZdSd3bbpTxSIRJ1jL6JI6rttQydi91QS9cZiR38A9/tt6DFpERA6iYlEbFgiFmb9qD09/tIWFG/bjdRsmD87nmrHdGNMzUz2JRJzSUAWfvhAZtHr/+sgN+Phvw4hrNJWxdDh7K+t5bsk2nl20ld2V9WSluAj2eA9Xjw9xJahgJOKUPhUNfGNjNedsL8OFi8DAC4gbfzsUFILuIUVEOjwVi9qgXRV1zF68jecWb2VvVQNd0hO4amw3Li/sSnZKnNPxRDqmcAg2vQefzIbVr0KwDvKHw4TvwMCLwe1xOqGIo4KhMP9es5eH5y1h6W4XhhDx+avw9i/Ck71J301FHJJTF+SaTVV8bXMZScEw9ZldiRv+DcywKyCtwOl4IiLiEBWL2ohAKMyC9SXMXryV+av3EraW0/tlM21cd87on4Nbj5qJOGPvmshg1cufh6qdkSnvB18Kw67Sr7Mih7H2zcew1/6c2UMn84+BZ1ORkEqibzecUkxctxW44mucjijSISUFwpyzs5oLt9cwYn8NFkOwx6l4h0+Dgf8FcclORxQRkZNIxaIY5g+GWbChhDeW7+KtVXuoqAuQmeTj8sKuXD22G10zE52OKNIx1eyHFS/Csmdh58dg3ND3HBh2JfSbrBlmRI5g7ZuPkT/lRlKqQ9R7fLw6YCJPj7qA5Xn9MTZMQvomTO9V+Lqs1mNqIg7pUhPgoh11TN5aRkFtgKA3HnPKxbiHXQ09TgOXy+mIIiLSylQsijENwRAL1pfw+vLdzFu1m8r6IClxHiadksv5Q/L5Sr9OxHncTscU6Xhq9sP6+bD6FVj7JoQDkDc0UiAachkkZzudUKRNaF4sau6zTt15ZdBE/tV3AhuyugFh4tO34Oq5kriC1bgSqpwJLNKRWcvw0nou3l7HWTvKSQ6GaUjJxjv0alz9z4/0oHXpvlREpD1SsSgG1AdCvL+uhH9+uot5q/dQVR8kJd7DOafkcsGQfCb2VYFI5KSzFvashLX/gnVvwfYlYMOQnAdDpsDwqyB3kNMpRdqcLyoWNbcuqysvDz6NN/tMYF2n7kCYhLQtmJ6r8RWswp1YefICiwgAcaEwp++u5aLtNYzeW4XHQiA+FXff83D1mwx9zoaEDKdjiojICaJikcPW7qni6w8spLohSGq8h3MH5XHBkHwm9OmEz6MuviInlb8WNv3nQIGockekPX945PGyfudC/gh1vxf5ElpSLGpufVYBLw86jbf6nMpn2T0BSEzYQbjrJry5G/Fmb8F4Aq0ZWUQOkRwIMX5vHWfsbWDsnkoy/CHCxkW462g8/c6PXDOz+2vcPhGRNkzFIocFQ2Hufm0VZw3I4dTeKhCJnFShAOxeDlsXwcZ3IoWiYD14k6D3mdDvPOh7LqTkOZ1UpN041mJRcxsyu/D6gFP5oMcIPu48kIDbi4sg3oxtuDpvwpuzEU/mDoz72D9bRI6Py1oGldVz5t4A43dX0K+yAQB/Wj6evufj6jERuo2H1HyHk4qIyLFQsUhEOo76isjjZFs/irx2FEOgNrIvo2ekONTvPOg+ATxxzmYVaae+TLGouTpPHEUFA3m3z3AWdRnGytzeWOPCbRrwdtqMK38z3pxNuNP2qHgkchLl1gX4yp56Ju6tZdS+ahJCke8QgbTOeLpPxHQdB93GQfZA9dQVEYlhKhaJSPtkLZRvgW1LYFu0OLRnJWDBuCBvCHQdB93GRpZpXZxOLNIhnKhi0aEq4pJY0H0o7/cezqIuQ9mY1RUAF0F8ybuxObvwZO7Ak7kDd+o+jCt8Qv++iHyeJ2zpX9HAqLIAw/bXMaS0lqyGIADBuGRM17G4u42P9DzKGwrxqQ4nFhGRRi0tFnlORhgRkeNSXwl7V8OeFZGCUOPLH509yZccmbHljB9B17GR9bgUZzOLyAmV1lDD+Ws/5Py1HwKwOzmL4i79Wdq1H6uy+7Bi/0Cq4kYD4DJ+vGm7MJ0iBSR3xk7cyaXqgSRyggVdhpUZ8azMiIdeKWAtBbVBRu73M6KsgSG736fn+n83HR9I64I7byiu3CGRSSRyB0NmT824JiISw9SzSEScV18JZZtg/4ZocWhlpEBUvuXAMXFp0RvMQZB7CnQeGbnZdKvmLRILWqtn0dGEMWzJyGdpl7580qUvqzv1YWVub+q8CQAYQvjiS7EZJbhSS3Cn7sOdWoI7pQSXr/6kZhXpSNL8IYaU1TOoMkzvynp6VdTRrdpPY3ko7IkjnDMAT+7QyPU8ux9k9oLUAl3bRURakXoWiUjssBZq9kHpRijdFCkMNS03Qu3+A8caF2T1hS6jYOT0yA1k7iBIK9DsKyLyOS4sPct20rNsJ5eueA+AkHGxIauAT/N6sTanK5syCtiUXsCmjHHUu71N7/V6KnGllkD6ftxJZbiSynElVuBKLMcVX41xxd4PaiJtRYXPzQe5SXyQCxDp9RsXCtOzys/AyjD9qvz0rFhH35UrSP/4QJE57HITTuuCO7MPJrN3pAdSRs/osgdEC8EiItK6VCwSkS8nFICq3dHXzsiycufB2xU7IFDT7E0G0rpCZg8YcOHBN4Kd+ulGUES+FLcN069kK/1Kth7UHjQutqXnsS6rgDW5XdmUWcDmtAI2ZvWn4pAxVQxBvHEV2JQKXEnRV2I5roQqXHHVmPgaXHE1esRN5Bg0uF2sSY9nTTpAIpAO1tKpIUT3aj89ai3dakLk15TTuWQBXbe+R3Lg4HMskNQJk9oZd2oXTEpnSMmPzMiWkgcpnSPLhAz9wCQi8iWpWCQiB4TD4K+GujKoK430+Kk9dBl91ZVB9R6oKQEO+fXd5Y3cvKXkQc5A6H32wQWh9G6alUxETjqPDTf1Qjp3/eKD9lX7EtiZms321Gw2Z+WyMy2bXUnZ7EnOZntaAXuThhI+zPgqHnctLl81NrEGk1AT6ZEUX4PLV4Px1WN8dbh8dRhvZN1469VjSaQ5YyiJ91AS76G4qTFavLWWtECYgpoA3WtCdK+15Nf6yazfQKeda8hpCJPmD37uI8MeH6HkHFyJnXAl5WASsyAxK1JEalxPzILEzMgyPk33JSIihzhqscgYMwUoB0Zaa/+nJftb2iYiX0IoCMF6CDZEpolvetWBv/bgtsbthkpoqIqMEdRQdch2dP3Qwk8Tc/BNVnp36DIy8itean60OBR9JWZp2lwRaVOS/XUHeiNt/Pz+oHGxOyWLvcmZ7E1KZ3daJvuS0ilNTKc0Po3ShHT2JadTktiT6rikI/4tt6sOlzdSOLLxDeD1YzwNGK8f44muew5t84M7gHEHm5bGHYDoUrPASbtkDBU+NxU+NyszDn+I12VHpwAACSZJREFULxQmuz5Edn2Q/AbIrQ+TXR8kq76alIYy0vauJsMfJt0fIj70xedJ2O0lHJcMcamYuFRc8emYuNTITG5xKRCXCr6kyMubAN7EyMuXeGDdmxDZ74mPvuLUw0lE2qwjFouiBR6stfONMb2MMZOstfOPtB9Ib0lb889pl0JBqN594j+3xQOSt/C4L/N5X/he24Jjmu+zR9/+3HrzY+xhls2OteEvOCYcfdkDy8O2hyLLcCja1nw7ur9xPRyMrIeDB9qbtzUuQ34IByL/nYQDke1D10N+CDVEikHBegj6I8tQdGmP44uBJyFyw9P8xicpO7JsakuBhMwDv7Y1vuLTNGuJiHRYHhumoHIfBZX7jnpsvdtLRUIKFfHJVMQlU5qYTGlSMuUJKVTGJ1MZl0SVL5mquGSqvEnU+uKojutErS+eGm9C0+Dcx8IQwuUKYFxBjCsIrhDGFcK6g+AOgzuEdYUij825ghhXCFxhjIksMeHodhhcITDhSAHKRF7GhMHYZtuN69Glyx44Bhttj6ybxnUTPrAPIu1YMBzU3vQZTesc+Bw4+D1N/wMccg/xBfsNh7Y3rhzmfsUcpu2wvuC4w9YIHOpV1uJ/S9tTB2w1sDUBOMqpExcKkxYIkhEIku4PkhWEjECI1ECYpFCIpECQxFA1icFykso3kRIMkxwMNe07nrugsMtL2O3FuuOwbh/WE4d1x0UKSe7oy+UFlwfr8oLbG1m6PFi3F1yN226sywPG/fl1446+3x1pMy4wbqwxn992NdvGRIpZxgVEl8YVfV9jmzmwNK7Iez7XfmDdNv2H36wdDhTNmrc1b286O81h2w9uowX7vkgLjzumIl/LjrUqHLZpLpebnC49nY5xUh2tZ9FoYE50fSMwEph/lP1ZLWxr38Wiyu3wp2FOp5CYYMDliV6c3eCO3AgQvSH43LrbFznemxb9VcoXuZHwNHu5D1lv/qvW4X7havwFrNnAriIiJ5o30H6/kB6L+FCA+OpScqtLj+v9YQx13jhqfPHUehOo9iVQ60ugzuOj3uOjwRsXWbq9TeuRV2Q94Pbgd3vxR5cBt/egtoDbh9/tJejyEHS5CLo9BI2bULP1oNtNQNcMaYf2HPc7LXEESKCBRBpIMA0k0EACfhJNA/HR9sb1OIL4TAAfQeII4CMQWR7U1oDX1OIliIcQvujSQxCvCTW1R5Zh3IRxE8Jj1JNQ5GQrtSkEf7oejzfe6SgnzdGKRemHbGe1YH9L2w5ijJkBzADo1q3bUWK1AYlZcNH9mFHXOp1ERERE2hQLgfrIi3Knw4iIiAiVVN1RSnJGZ6eDnDRHKxaVA5nHuL+lbQex1s4EZgIUFha2/Z8m41Jg5HSsne50EhERERERERGRFjtasWgJB3oF9QLmtWB/egvbREREREREREQkxhxxuiJr7VygcZBqGgelNsbM+6L9LW1rrX+QiIiIiIiIiIgcP2NbPBvWyVNYWGiLioqcjiEiIiIiIiIi0m4YY4qttYVHO+6IPYtERERERERERKRjUbFIRERERERERESaqFgkIiIiIiIiIiJNVCwSEREREREREZEmKhaJiIiIiIiIiEgTFYtERERERERERKSJikUiIiIiIiIiItLEWGudzvA5xph9wBanc5wgnYASp0OIyEF0XorEJp2bIrFH56VIbNK5Kceru7U2+2gHxWSxqD0xxhRZawudziEiB+i8FIlNOjdFYo/OS5HYpHNTWpseQxMRERERERERkSYqFomIiIiIiIiISBMVi1rfTKcDiMjn6LwUiU06N0Vij85Lkdikc1NalcYsEhERERERERGRJupZJCIiIiIiIiIiTVQsEhERERERERGRJioWiYiIiIiIiIhIExWLWokxZooxZpIx5gdOZxGRA4wxZcaYYmPMfU5nEenootfJeYe06fop4qAvOC917RRxkDEmPXp9nNL8PNQ1U1qTikWtwBgzBcBaOx8oN8ZMcjiSiBxwmbV2lLX2h04HEenootfJJrp+ijjv0PMyStdOEWddDmRaa+cCGGNm6JoprU3FotYxGtgYXd8IjHQwi4gcLN0Y08vpECJyWLp+isQmXTtFHGStnWmtnRnd7AXMR9dMaWUqFrWO9EO2sxxJISKHkwmUGmMedjqIiHyOrp8isUnXTpEYEC3allprN6JrprQyFYtaRzmRi6qIxJjoLzPlRLrrTnE6j0isiY59cF+0i/uM6DgJJ2ucEl0/RWKQrp0iMWOKtfbG6LqumdKqPE4HaKeWcKDS2wuYd4RjReQkMcbMIPJrzFxgv9N5RGJN9Evgj621o6LbI4Fi4GT1JtD1UyTG6NopEhuMMVOstf8TXZ+ErpnSytSzqBVEL6a9GgcZ+4KBAkXk5HueZgMANg4SKCJNXdtfAC5rbLPWLuXA2AiNx00yxhSfoL85BShsNkinrp8iDjv0vETXThHHRc+/+6KzEhaDrpnS+oy11ukMIiIi4jBjzAtAurX2nGZtk4B51lrTbLsUKG5sExEREZH2Rz2LREREBGAKn+/Cfg7NehVZa+dHexuJiIiISDumYpGIiEgH12xK7EMLQZMO0yYiIiIi7ZwGuBYREZFGRY0rxph0YCTww9b4Q42D5kY3ezUO2ikiIiIizlPPIhERkQ7OWrsR2EhkMOtGj0T3nfABM40x90U/e250gM7expiRjYN0ioiIiIiz1LNIREREIDI+0Q+bzXRWyjE8ghbtKdT7CIfMs9bOjz7yNsVa2/zYDUQeedt4jJlFREREpBWoWCQiIiKNvYtubNyOFo1a3KvIWjuzhYdO+oLPPaf5TGwiIiIi4hw9hiYiIiKHM5LPz452ImwEyg9p691Kf0tEREREjoOKRSIiInIQY8zI6GrRIe2TGscbMsbcdzxjDDWOgRT9rJHGmCnAfUCWxiwSERERiQ3GWut0BhEREYkRxpiHiTwq1guYCdwXfURNRERERDoIFYtERERERERERKSJHkMTEREREREREZEmKhaJiIiIiIiIiEgTFYtERERERERERKSJikUiIiIiIiIiItJExSIREREREREREWmiYpGIiIiIiIiIiDRRsUhERERERERERJqoWCQiIiIiIiIiIk1ULBIRERERERERkSb/H/Frpb0HtxJYAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<Figure size 1440x360 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "power_alpha(0.01)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Lassen wir $\\alpha$ kleiner werden, so nimmt zwar der Fehler 1. Art ab, aber der Fehler 2. Art nimmt zu und damit nimmt die Macht (das was wir wollen) ab. \n",
+    "\n",
+    "Die Wahl von $\\alpha$ ist immer eine Abwägung von kleinem Fehler 1. Art und grosser Macht."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.7"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
-- 
GitLab