{
"cells": [
{
"cell_type": "markdown",
"id": "33033e5d-244a-4bf0-8027-5f4d5173b267",
"metadata": {},
"source": [
"## Hypothesentests\n",
"----------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "3a7f4368-02eb-4738-9597-073996d7447f",
"metadata": {},
"source": [
"Ein sehr häufiges Problem, mit dem Wissenschaftler konfrontiert sind, ist die **Bewertung der Signifikanz** von verstreuten statistischen Daten. Aufgrund der begrenzten Verfügbarkeit von Beobachtungsdaten wenden Wissenschaftler inferenzstatistische Methoden an, um zu entscheiden, ob die beobachteten Daten signifikante Informationen enthalten oder ob die verstreuten Daten nichts weiter als die Manifestation der inhärent probabilistischen Natur des Datenerzeugungsprozesses sind.\n",
"\n",
"Im Allgemeinen formuliert ein Wissenschaftler ein solches Problem wie folgt. Der Wissenschaftler erstellt ein Modell, das lediglich eine Vereinfachung des Datenerzeugungsprozesses darstellt, und betrachtet eine bestimmte Annahme - eine so genannte Hypothese - dieses Modells. Anhand von Daten will er diese vorläufige Hypothese bewerten.\n",
"\n",
"Bei der Hypothesenprüfung geht es darum, **auf der Grundlage von Stichproben aus der Grundgesamtheit statistische Rückschlüsse auf diese Grundgesamtheit zu ziehen**. Eine Möglichkeit zur Schätzung eines Grundgesamtheitsparameters ist die Erstellung von Konfidenzintervallen. Eine andere Möglichkeit besteht darin, eine Entscheidung über einen Parameter in Form eines Tests zu treffen. Jeder Hypothesentest erfordert die Erhebung von Daten (Stichproben). Wenn die Hypothese als richtig angenommen wird, kann der Wissenschaftler die erwarteten Ergebnisse eines Experiments berechnen. Weichen die beobachteten Daten erheblich von den erwarteten Ergebnissen ab, so gilt die Annahme als falsch. Auf der Grundlage der beobachteten Daten trifft der Wissenschaftler also eine Entscheidung darüber, ob es aufgrund der Analyse der Daten genügend Beweise dafür gibt, dass das Modell - die Hypothese - verworfen werden sollte, oder ob es keine ausreichenden Beweise für die Verwerfung der angegebenen Hypothese gibt."
]
},
{
"cell_type": "markdown",
"id": "00dab745-100c-4755-b663-bb3d1733ae06",
"metadata": {},
"source": [
"## Einführung in Hypothesentests\n",
"----------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "037af377-642e-4976-8ddd-b34fd3cf7f21",
"metadata": {},
"source": [
"In der **Inferenzstatistik** geht es darum, Entscheidungen oder Urteile über den Wert einer bestimmten Beobachtung oder Messung zu treffen. Eine der am häufigsten verwendeten Methoden, um solche Entscheidungen zu treffen, ist die Durchführung eines Hypothesentests. Eine Hypothese ist ein Erklärungsvorschlag für ein Phänomen. Im Zusammenhang mit statistischen Hypothesentests ist der Begriff Hypothese eine Aussage über etwas, von dem angenommen wird, dass es wahr ist.\n",
"\n",
"Zu einem Hypothesentest gehören zwei Hypothesen: die **Nullhypothese** und die **Alternativhypothese**. Die Nullhypothese ($H_0$) ist eine zu prüfende Aussage. Die Alternativhypothese ($H_A$) ist eine Aussage, die als Alternative zur Nullhypothese betrachtet wird.\n",
"\n",
"Mit dem Hypothesentest soll geprüft werden, ob die Nullhypothese zugunsten der Alternativhypothese verworfen werden sollte. Die grundlegende Logik eines Hypothesentests besteht darin, zwei statistische Datensätze zu vergleichen. Ein Datensatz wird durch eine Stichprobe gewonnen, der andere Datensatz stammt aus einem idealisierten Modell. Wenn die Stichprobendaten mit dem idealisierten Modell übereinstimmen, wird die Nullhypothese nicht verworfen; wenn die Stichprobendaten nicht mit dem idealisierten Modell übereinstimmen und somit eine Alternativhypothese unterstützen, wird die Nullhypothese zugunsten der Alternativhypothese verworfen.\n",
"\n",
"Das Kriterium für die Entscheidung über die Ablehnung der Nullhypothese ist eine so genannte Teststatistik. Die Teststatistik ist eine Zahl, die aus dem Datensatz berechnet wird, der durch Messungen und Beobachtungen oder, allgemeiner, durch Stichproben gewonnen wird."
]
},
{
"cell_type": "markdown",
"id": "a6c0ea8b-2792-49de-9fac-c2b816259c98",
"metadata": {},
"source": [
"## Formulierung der Hypothese\n",
"----------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "919234d7-595b-4498-9ebe-a510ca05595b",
"metadata": {},
"source": [
"Jeder Hypothesentest beginnt mit der Formulierung der Nullhypothese und der Alternativhypothese. Dieser Abschnitt konzentriert sich auf Hypothesentests für einen Grundgesamtheitsmittelwert, $\\mu$ jedoch gilt das allgemeine Verfahren für jeden Hypothesentest.\n",
"\n",
"Die Nullhypothese für einen Hypothesentest für einen Mittelwert der Grundgesamtheit, $\\mu$\n",
"wird ausgedrückt als"
]
},
{
"cell_type": "markdown",
"id": "49a45dac-48dd-4f91-b6a4-3be90d05152b",
"metadata": {},
"source": [
"$$ H_0: \\mu = \\mu_0, $$"
]
},
{
"cell_type": "markdown",
"id": "9dc5b2fd-8734-4c62-9515-49615b3ab6a8",
"metadata": {},
"source": [
"wobei $\\mu_0$ eine Zahl ist.\n",
"\n",
"Die Formulierung der Alternativhypothese hängt vom Zweck des Hypothesentests ab. Es gibt drei Möglichkeiten, eine Alternativhypothese zu formulieren ({cite:t}`fahrmeirstatistik` s.369, {cite:t}`Bruce2021` s.97).\n",
"\n",
"Wenn es bei dem Hypothesentest darum geht, zu entscheiden, ob ein Grundgesamtheitsmittelwert von dem angegebenen Wert $\\mu_0$ abweicht, wird die Alternativhypothese wie folgt formuliert"
]
},
{
"cell_type": "markdown",
"id": "0bcfcd49-84b1-4632-9efd-aadce370b3d0",
"metadata": {},
"source": [
"$$H_A: \\mu \\ne \\mu_0\\text{.}$$"
]
},
{
"cell_type": "markdown",
"id": "e40cc0ef-c297-489d-bf89-86222b53b010",
"metadata": {},
"source": [
"Ein solcher Hypothesentest wird als **zweiseitiger Test** bezeichnet.\n",
"\n",
"Wenn es bei dem Hypothesentest darum geht, zu entscheiden, ob der Mittelwert der Grundgesamtheit, $\\mu$\n",
"kleiner ist als der angegebene Wert $\\mu_0$, wird die Alternativhypothese wie folgt ausgedrückt"
]
},
{
"cell_type": "markdown",
"id": "5edc437e-c1f9-418f-89e7-c9c29a8a3e7f",
"metadata": {},
"source": [
"$$H_A: \\mu < \\mu_0\\text{.}$$"
]
},
{
"cell_type": "markdown",
"id": "1a2fe1d8-377c-44b8-a3a0-29973d8c5ef5",
"metadata": {},
"source": [
"Ein solcher Hypothesentest wird als **linksseitiger Test** bezeichnet.\n",
"\n",
"Geht es bei dem Hypothesentest darum, zu entscheiden, ob der Mittelwert der Grundgesamtheit, $\\mu$\n",
"größer als ein bestimmter Wert $\\mu_0$ ist, wird die Alternativhypothese wie folgt ausgedrückt"
]
},
{
"cell_type": "markdown",
"id": "7e59f4d6-f62c-4ce2-8a28-e11a82cce0db",
"metadata": {},
"source": [
"$$H_A: \\mu > \\mu_0\\text{.}$$"
]
},
{
"cell_type": "markdown",
"id": "dfc9c1a2-552f-4a92-82a4-dd7fb65e5f2f",
"metadata": {},
"source": [
"Ein solcher Hypothesentest wird als **rechtsseitiger Test** bezeichnet.\n",
"\n",
"Man beachte, dass ein Hypothesentest als **einseitiger** Test bezeichnet wird, wenn er entweder \"linksseitig\" oder \"rechtsseitig\" ist."
]
},
{
"cell_type": "markdown",
"id": "38ccdcd2",
"metadata": {},
"source": [
"||zweiseitiger Test|linksseitiger Test|rechtsseitiger Test|\n",
"|---|:---:|:---:|:---:|\n",
"|Beziehung zwischen $\\mu$, $\\mu_0$ Ablehnung |$\\ne$| $\\lt$| $\\gt$|"
]
},
{
"cell_type": "markdown",
"id": "785c1901-9f92-4c18-968f-f67b6e6c280c",
"metadata": {},
"source": [
"## Fehler vom Typ I, Fehler vom Typ II und Signifikanzniveau\n",
"----------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "e8b32da4-2737-4c6e-a0e3-092897374d42",
"metadata": {},
"source": [
"Jede Entscheidung, die auf der Grundlage eines Hypothesentests getroffen wird, kann falsch sein. Im Rahmen von Hypothesentests gibt es zwei Arten von Fehlern: Fehler vom Typ I und Fehler vom Typ II. Ein Fehler vom Typ I tritt auf, wenn eine wahre Nullhypothese abgelehnt wird (ein \"falsches Positiv\"), während ein Fehler vom Typ II auftritt, wenn eine falsche Nullhypothese nicht abgelehnt wird (ein \"falsches Negativ\"). Mit anderen Worten, ein Fehler vom Typ I besteht darin, dass ein Effekt festgestellt wird, der nicht vorhanden ist, während ein Fehler vom Typ II darin besteht, dass ein Effekt nicht festgestellt wird, der vorhanden ist."
]
},
{
"cell_type": "markdown",
"id": "097a3a64",
"metadata": {},
"source": [
"||$H_0$ trifft zu|$H_0$ trifft nicht zu|\n",
"|---|---|---|\n",
"|$H_0$ nicht ablehnen|korrekte Entscheidung|Typ II Fehler|\n",
"|$H_0$ ablehnen|Typ I Fehler|korrekte Entscheidung|\n"
]
},
{
"cell_type": "markdown",
"id": "a7ad52e5-8d7d-409f-870f-b24469cddcfb",
"metadata": {},
"source": [
"Wenn Sie sich nicht sicher sind, ob es sich um einen Fehler des Typs I oder des Typs II handelt, hilft Ihnen vielleicht eine Illustration (hier)."
]
},
{
"cell_type": "markdown",
"id": "5492bf4b-a43c-4604-bf9f-98ea97cc7ffe",
"metadata": {},
"source": [
"Die Durchführung eines Hypothesentests bedeutet immer, dass die Möglichkeit besteht, eine falsche Entscheidung zu treffen. Die Wahrscheinlichkeit eines Fehlers vom Typ I (eine wahre Nullhypothese wird abgelehnt) wird allgemein als Signifikanzniveau des Hypothesentests bezeichnet und mit $\\alpha$ angegeben. Die Wahrscheinlichkeit eines Fehlers vom Typ II (eine falsche Nullhypothese wird nicht abgelehnt) wird mit $\\beta$ angegeben. Beachten Sie, dass bei einem festen Stichprobenumfang die Wahrscheinlichkeit $\\beta$ umso größer ist, je kleiner das Signifikanzniveau $\\alpha$ ist, eine falsche Nullhypothese nicht zurückzuweisen ({cite:t}`fahrmeirstatistik` s.385).\n",
"\n",
"Das Ergebnis eines Hypothesentests ist eine Aussage zu Gunsten der Nullhypothese oder zu Gunsten der Alternativhypothese. Wenn die Nullhypothese abgelehnt wird, liefern die Daten genügend Beweise, um die Alternativhypothese zu stützen. Wenn die Nullhypothese nicht verworfen wird, liefern die Daten keine ausreichenden Beweise für die Alternativhypothese. Wenn der Hypothesentest auf dem Signifikanzniveau $\\alpha$ durchgeführt wird, kann man sagen, dass die Testergebnisse auf dem **$\\alpha$-Niveau statistisch signifikant sind**. Wenn die Nullhypothese auf dem Signifikanzniveau $\\alpha$ nicht abgelehnt wird, kann man sagen, dass die Testergebnisse auf dem **$\\alpha$-Niveau statistisch nicht signifikant sind**."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "085096d6-2269-4157-8f2f-02c0c2b0141e",
"metadata": {
"tags": [
"remove-cell"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"---------------------------------\n",
"Working on the host: Joachims-MacBook-Pro.local\n",
"\n",
"---------------------------------\n",
"Python version: 3.10.2 | packaged by conda-forge | (main, Feb 1 2022, 19:30:18) [Clang 11.1.0 ]\n",
"\n",
"---------------------------------\n",
"Python interpreter: /opt/miniconda3/envs/srh/bin/python\n"
]
}
],
"source": [
"%matplotlib inline\n",
"# Load the \"autoreload\" extension\n",
"%load_ext autoreload\n",
"# always reload modules\n",
"%autoreload 2\n",
"# black formatter for jupyter notebooks\n",
"#%load_ext nb_black\n",
"# black formatter for jupyter lab\n",
"%load_ext lab_black\n",
"\n",
"%run ../../src/notebook_env.py"
]
},
{
"cell_type": "markdown",
"id": "bdf9fd31-7e55-4a39-bebf-49a7ed689bc6",
"metadata": {},
"source": [
"## Der kritische Wert und der $p$-Wert-Ansatz bei der Hypothesenprüfung\n",
"----------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "e9378559-f4e8-4801-b916-9fbb027ac88a",
"metadata": {},
"source": [
"Um zu entscheiden, ob die Nullhypothese abzulehnen ist, wird eine **Teststatistik** berechnet. Die Entscheidung wird auf der Grundlage des numerischen Wertes der Teststatistik getroffen. Es gibt zwei Ansätze, um zu dieser Entscheidung zu gelangen: Der Ansatz des **kritischen Wertes** und der Ansatz des **$p$-Wertes**."
]
},
{
"cell_type": "markdown",
"id": "fce48c4d-6494-4003-b9cf-42fce512fd81",
"metadata": {},
"source": [
"### Der Ansatz des kritischen Wertes"
]
},
{
"cell_type": "markdown",
"id": "6d06587c-2d0c-4239-a5d7-a6f823447166",
"metadata": {},
"source": [
"Mit dem Ansatz des **kritischen Wertes** wird festgestellt, ob die beobachtete Teststatistik zu stark von einem definiertem kritischen Wert abweicht oder nicht. Dazu wird die beobachtete Teststatistik (berechnet auf der Grundlage der Stichprobendaten) mit dem kritischen Wert, einer Art Grenzwert, verglichen. Wenn die Teststatistik extremer ist als der kritische Wert, wird die Nullhypothese abgelehnt. Wenn die Teststatistik nicht so extrem ist wie der kritische Wert, wird die Nullhypothese nicht verworfen. Der kritische Wert wird auf der Grundlage des vorgegebenen Signifikanzniveaus $\\alpha$ und der Art der Wahrscheinlichkeitsverteilung des idealisierten Modells berechnet. Der kritische Wert teilt die Fläche unter der Wahrscheinlichkeitsverteilungskurve in die **Ablehnungsregion(en)** und in die **Nichtablehnungsregion**.\n",
"\n",
"Die folgenden drei Abbildungen zeigen einen rechtsseitigen Test, einen linksseitigen Test und einen zweiseitigen Test. Das idealisierte Modell in den Abbildungen, und damit $H_0$ wird durch eine glockenförmige normale Wahrscheinlichkeitskurve beschrieben.\n",
"\n",
"Bei einem **zweiseitigen** Test wird die Nullhypothese abgelehnt, wenn die Teststatistik entweder zu klein oder zu groß ist. Der Ablehnungsbereich für einen solchen Test besteht also aus zwei Teilen: einem links und einem rechts."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "b771924c-85a8-4aca-962e-c2b9fd299039",
"metadata": {
"tags": [
"hide-cell"
]
},
"outputs": [],
"source": [
"import numpy as np\n",
"\n",
"\n",
"def range_brace(\n",
" x_min,\n",
" x_max,\n",
" mid=0.75,\n",
" beta1=50.0,\n",
" beta2=100.0,\n",
" height=1,\n",
" initial_divisions=11,\n",
" resolution_factor=1.5,\n",
"):\n",
" # determine x0 adaptively values using second derivitive\n",
" # could be replaced with less snazzy:\n",
" # x0 = np.arange(0, 0.5, .001)\n",
" x0 = np.array(())\n",
" tmpx = np.linspace(0, 0.5, initial_divisions)\n",
" tmp = (\n",
" beta1**2\n",
" * (np.exp(beta1 * tmpx))\n",
" * (1 - np.exp(beta1 * tmpx))\n",
" / np.power((1 + np.exp(beta1 * tmpx)), 3)\n",
" )\n",
" tmp += (\n",
" beta2**2\n",
" * (np.exp(beta2 * (tmpx - 0.5)))\n",
" * (1 - np.exp(beta2 * (tmpx - 0.5)))\n",
" / np.power((1 + np.exp(beta2 * (tmpx - 0.5))), 3)\n",
" )\n",
" for i in range(0, len(tmpx) - 1):\n",
" t = int(\n",
" np.ceil(\n",
" resolution_factor\n",
" * max(np.abs(tmp[i : i + 2]))\n",
" / float(initial_divisions)\n",
" )\n",
" )\n",
" x0 = np.append(x0, np.linspace(tmpx[i], tmpx[i + 1], t))\n",
" x0 = np.sort(np.unique(x0)) # sort and remove dups\n",
" # half brace using sum of two logistic functions\n",
" y0 = mid * 2 * ((1 / (1.0 + np.exp(-1 * beta1 * x0))) - 0.5)\n",
" y0 += (1 - mid) * 2 * (1 / (1.0 + np.exp(-1 * beta2 * (x0 - 0.5))))\n",
" # concat and scale x\n",
" x = np.concatenate((x0, 1 - x0[::-1])) * float((x_max - x_min)) + x_min\n",
" y = np.concatenate((y0, y0[::-1])) * float(height)\n",
" return (x, y)"
]
},
{
"cell_type": "code",
"execution_count": 88,
"id": "342b3a95-0317-4c19-8dea-2468b269d07e",
"metadata": {
"tags": [
"hide-cell"
]
},
"outputs": [
{
"data": {
"text/plain": [
"(-0.05, 0.5)"
]
},
"execution_count": 88,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import norm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"fig, ax = plt.subplots(figsize=(16, 8))\n",
"x_min = -4\n",
"x_max = 4\n",
"x = np.linspace(x_min, x_max, 1000)\n",
"\n",
"mu = 0\n",
"sigma = 1\n",
"ax.plot(x, norm.pdf(x), color=\"C0\", linewidth=2)\n",
"\n",
"\n",
"ticks = [-1.5, 1.5]\n",
"for _x in ticks:\n",
" ax.axvline(_x, linestyle=\"dashed\")\n",
"\n",
"ax.axhline(0)\n",
"ax.axis(\"off\")\n",
"\n",
"ax.fill_between(x, norm.pdf(x), where=x <= ticks[0], color=\"r\", alpha=0.5)\n",
"ax.fill_between(x, norm.pdf(x), where=x >= ticks[1], color=\"r\", alpha=0.5)\n",
"\n",
"x, y = range_brace(\n",
" ticks[0],\n",
" ticks[1],\n",
" height=0.05,\n",
")\n",
"ax.plot(x, -y, \"--\", color=\"k\")\n",
"\n",
"x, y = range_brace(\n",
" x_min,\n",
" ticks[0],\n",
" height=0.05,\n",
")\n",
"ax.plot(x, -y, \"--\", color=\"k\")\n",
"\n",
"x, y = range_brace(\n",
" ticks[1],\n",
" x_max,\n",
" height=0.05,\n",
")\n",
"ax.plot(x, -y, \"--\", color=\"k\")\n",
"\n",
"ax.text(s=\"Ablehnen der $H_0$\", x=-3.9, y=0.45, size=26)\n",
"ax.text(s=\"Ablehnen der $H_0$\", x=2, y=0.45, size=26)\n",
"ax.text(s=\"Nicht ablehnen der $H_0$\", x=-1.2, y=0.45, size=26)\n",
"\n",
"\n",
"ax.text(s=\"Region der Ablehnung\", x=-3.9, y=-0.08, size=18)\n",
"ax.text(s=\"Region der Ablehnung\", x=2, y=-0.08, size=18)\n",
"ax.text(s=\"Region der Nicht-Ablehnung\", x=-1.2, y=-0.08, size=18)\n",
"\n",
"ax.text(s=r\"$1-\\alpha$\", x=-0.3, y=0.25, size=22)\n",
"\n",
"ax.annotate(\n",
" r\"$\\alpha/2$\",\n",
" xy=(2, 0.02),\n",
" xytext=(2.4, 0.1),\n",
" # textcoords=\"data\",\n",
" arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n",
" size=19,\n",
")\n",
"\n",
"ax.annotate(\n",
" r\"$\\alpha/2$\",\n",
" xy=(-2, 0.02),\n",
" xytext=(-2.6, 0.1),\n",
" # textcoords=\"data\",\n",
" arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n",
" size=19,\n",
")\n",
"\n",
"ax.annotate(\n",
" r\"Kritischer Wert\",\n",
" xy=(ticks[1], 0.3),\n",
" xytext=(2.2, 0.3),\n",
" # textcoords=\"data\",\n",
" arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n",
" size=19,\n",
" verticalalignment=\"center\",\n",
")\n",
"\n",
"ax.annotate(\n",
" r\"Kritischer Wert\",\n",
" xy=(ticks[0], 0.3),\n",
" xytext=(-3.4, 0.3),\n",
" # textcoords=\"data\",\n",
" arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n",
" size=19,\n",
" verticalalignment=\"center\",\n",
")\n",
"\n",
"ax.set_ylim(-0.05, 0.5)"
]
},
{
"cell_type": "markdown",
"id": "48364017-9109-4842-ae28-7249c8b5c9b2",
"metadata": {},
"source": [
"Bei einem **linksseitigen Test** wird die Nullhypothese abgelehnt, wenn die Teststatistik zu klein ist. Der Ablehnungsbereich für einen solchen Test besteht also aus einem Teil, der links von der Mitte liegt."
]
},
{
"cell_type": "code",
"execution_count": 119,
"id": "d1a23eeb-66e2-4409-80e6-5afb309e8d22",
"metadata": {
"tags": [
"hide-cell"
]
},
"outputs": [
{
"data": {
"text/plain": [
"(-0.05, 0.5)"
]
},
"execution_count": 119,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import norm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"fig, ax = plt.subplots(figsize=(16, 8))\n",
"x_min = -4\n",
"x_max = 4\n",
"x = np.linspace(x_min, x_max, 1000)\n",
"\n",
"mu = 0\n",
"sigma = 1\n",
"ax.plot(x, norm.pdf(x), color=\"C0\", linewidth=2)\n",
"\n",
"\n",
"ticks = [-1.5]\n",
"for _x in ticks:\n",
" ax.axvline(_x, linestyle=\"dashed\")\n",
"\n",
"ax.axhline(0)\n",
"ax.axis(\"off\")\n",
"\n",
"ax.fill_between(x, norm.pdf(x), where=x <= ticks[0], color=\"r\", alpha=0.5)\n",
"\n",
"x, y = range_brace(\n",
" ticks[0],\n",
" x_max,\n",
" height=0.05,\n",
")\n",
"ax.plot(x, -y, \"--\", color=\"k\")\n",
"\n",
"x, y = range_brace(\n",
" x_min,\n",
" ticks[0],\n",
" height=0.05,\n",
")\n",
"ax.plot(x, -y, \"--\", color=\"k\")\n",
"\n",
"ax.plot(x, -y, \"--\", color=\"k\")\n",
"\n",
"ax.text(s=\"Ablehnen der $H_0$\", x=-3.9, y=0.45, size=26)\n",
"ax.text(s=\"Nicht ablehnen der $H_0$\", x=-1.2, y=0.45, size=26)\n",
"\n",
"\n",
"ax.text(s=\"Region der Ablehnung\", x=-3.9, y=-0.08, size=18)\n",
"ax.text(s=\"Region der Nicht-Ablehnung\", x=0.2, y=-0.08, size=18)\n",
"\n",
"ax.text(s=r\"$1-\\alpha$\", x=-0.3, y=0.25, size=22)\n",
"\n",
"\n",
"ax.annotate(\n",
" r\"$\\alpha$\",\n",
" xy=(-2, 0.02),\n",
" xytext=(-2.6, 0.1),\n",
" # textcoords=\"data\",\n",
" arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n",
" size=19,\n",
")\n",
"\n",
"\n",
"ax.annotate(\n",
" r\"Kritischer Wert\",\n",
" xy=(ticks[0], 0.3),\n",
" xytext=(-3.4, 0.3),\n",
" # textcoords=\"data\",\n",
" arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n",
" size=19,\n",
" verticalalignment=\"center\",\n",
")\n",
"\n",
"ax.set_ylim(-0.05, 0.5)"
]
},
{
"cell_type": "markdown",
"id": "3b9164da-4eb0-43b7-ae9d-4ac4ec5ffe9f",
"metadata": {},
"source": [
"Bei einem **rechtsseitigen Test** wird die Nullhypothese abgelehnt, wenn die Teststatistik zu groß ist. Der Ablehnungsbereich für einen solchen Test besteht also aus einem Teil, der sich rechts von der Mitte befindet."
]
},
{
"cell_type": "code",
"execution_count": 121,
"id": "e3c1f90a-d439-4d74-9163-5bea934c11f8",
"metadata": {
"tags": [
"hide-cell"
]
},
"outputs": [
{
"data": {
"text/plain": [
"(-0.05, 0.5)"
]
},
"execution_count": 121,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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ru3jtoL8XMxsDLB8me3w2KZSKlFpcfLSL1Uqtk46usmxMxTr9cS7FVh0fCD/AX0+2U3sfktfS0dplZVXUuhwXGu131pNGi7evxwUdE4YeJYsiIgModN78Q3rZsptz7kV81dX98SfdNvwx+7/AkcBqzrnn6xjqYcAfgHfwVVHnMd8tRncx/hP/XMel+D7HLMT4GPA7/PMcB4TVFzGzas9g7gLsjX9fY8P+LwXWdM5Vaymxu3jewj/nuTtwJ77J+3Fhm9cBmzrnOlVvK0Kjxeqcew74Iv7mxpP478AH+E6+v0hHn3LVXjvY7+XzdFSXrkdDFtDRBUC1amWlqnbVqqP1Sp7G5+ZpfG5/t9NgfhDG99TaTZBzbga+BAqqN3RTl+NCo/3OetJo8fb1uKBjwtBiPXRDIiIiIjKkme/u5mzgB5XJiJndgm9YZX7nXL9KEqIkWwAgT+N3e1pXRIozWMeEZqCSRRERERnursFX8967vETdzFYHNgSurNNF4eV0NGAlIo1rsI4JDa+/HT+LiIiINDXn3HtmlgCnAneZ2fn4/vx+ge9z7tdFxicig0vHhA5KFkVERGTYc86dZmbvA/sCJ+IbaLodOKCn7iBEZOjRMcFTsigiIiICOOcuoaOfOBEZ5nRM0DOLIiIiIiIiUoVKFkVEREQGxxlFByAi0hvqOkNEREREREQ6UTVUERERkUEQJdmSUZIt2fOaIiKNQdVQRURERAbHBWE8qcggRERqpZJFERERERER6UTJooiIiIiIiHSiZFFEREREREQ6UbIoIiIiIiIinaiBGxEREZHB8buiAxAR6Q31sygiIiIiIiKdqBqqiIiIyCCIkmyFKMlWKDoOEZFaqRqqiIiIyOA4M4wnFRmEiEitVLIoIiIiIiIinShZFBERERERkU6ULIqIiIiIiEgnShZFRERERESkEzVwIyIiIjI4flt0ACIivaF+FkVERERERKQTVUMVERERGQRRkq0WJdlqRcchIlIrVUMVERERGRwnhvGkAmMQEamZShZFRERERESkEyWLIiIiIiIi0omSRREREREREelEyaKIiIiIiIh0ogZuRERERAbHgUUHICLSG+pnUURERERERDpRNVQRERGRQRAl2bpRkq1bdBwiIrVSNVQRERGRwXFUGE8qMggRkVqpZFFEREREREQ6UbIoIiIiIiIinShZFBERERERkU6ULIqIiIiIiEgnauBGREREZHD8vOgARER6Q/0sioiIiIiISCcqWRQRkWEjSjIDImBN4PPh76WAeYG5gVHALGAm8A7wBpADjwOPAU/kadw2yGHLEBEl2UYAeRrfVnQsIiK1ULIoIiJDWpRk8wFbAt8ANgIWqvGlK1aZNyVKsnuAW4Gr8jR+uT5RyjBxUBgrWRSRpqBkUUREhpwoycYAWwA7ApsDrWWL3wYeBv4NPA+8BLwHfIwvVWwFxgILAosBy+JLIdcAlgbiMJwYJdk/gXOAi/I0/mTA35iIiMggUrIoIiJDRpRk8wN7AD+lowSxHV+Scx1wM/BMnsZ9emA/SrIlga/hSyo3B9YOw3FRkl0InJin8TP9ehMiIiINQg3ciIhI04uSbEHgQGA3YFyY/W/gXODSPI3fGIB9jgW+DfwEWD/MbgcuAo7I0/jZeu9TmluUZHcC5Gk8qdhIRERqo2RRRESaVkjYfg4kwDxh9k3A8cAdfS1B7EMcK4c4JuNr7bQBfwYOzNP4ncGIQRqfkkURaTZKFkVEpClFSfZN4FRgyTDrJuCAPI0fLTCmpfElnJPxSeOH+EZN/qBWVCVKshUA8jR+uuhYRERqoWRRRESaSpRkCwMnA98Lsx4FftVI3RFESbY8PsZNwqx/AT/I0/jx4qISERHpHSWLIiLSNKIk2wY4E98v4jTgAOC0Riy1C306bgWcCHwG39Lqr4HfN2K8MvCiJNsSIE/j64qORUSkFkoWRUSk4UVJNg74Pb4BG4BbgN3zNM4LC6pGUZLNBZwA/DjMugvYMU/jV4uLSoqgZxZFpNmMKDoAERGR7kRJthLwT3yiOBPYC9i0GRJFgDyNP8nTeDd8dxtvAV8FHo6S7GvFRiYiItI9JYsiItKwQiM2DwArA88A6+RpfPpgtXJaT3kaXw+sgu/zcSHgtijJfhWqq4qIiDQcJYsiItJwoiSzKMkS4GpgLuBSYM0iWzqth9CNxqbA0fhz8LHARVGSjS40MBERkSqULIqISEOJkmwUcB4+oTJ81xPb52n8SaGB1Umexm15Gh8IfBv4BNgeuCVKsvmKjUxEROTTlCyKiEjDCI3BXAfsBEwFvpOn8ZHNWO20J3kaXw2sD7wObADcFyXZMoUGJQNtpzCIiDQFtYYqIiINIUqyBYAMWBt4B9gsT+OHi41q4EVJtiT+fa8CvAlslKfxE8VGJSIiopJFERFpAFGSLQ7cg08Uc2C94ZAoAuRp/ArwFeAOYBHgrijJ1ig2KhkIUZJtGyXZtkXHISJSKyWLIiJSqJAo3gl8DvgPPlF8ttCgBlmexlOALYAbgPmBv0VJtm6xUckA2CMMIiJNQcmiiIgUpixRXBZ4BJiUp/HrhQZVkDyNp+MbvbkCmAff6I0SRhERKYySRRERKUSVRHGjPI3fLzSoguVpPAvYDrgIGA/cGCXZmsVGJSIiw5WSRRERGXRRks0P3IoSxU7yNJ4DTAb+SkcJ4yqFBiUiIsOSkkURERlUoXuMDFgReAIlip2EhHFHfDci8wG3RUm2XLFRiYjIcKNkUUREBk2UZKOAy4EvAS8BmyhRrC5USf0evgR2IeCmKMkWLjYq6afvhkFEpCmon0URERkUUZKNAC4Etsf3o/iVPI2fKTaqxhdKYv8GrAU8BHwtT+NPio1KRESGA5UsiojIYDkenyh+DGymRLE2ITHcAngBnzBeGiXZyGKjkr6IkmxylGSTi45DRKRWShZFRGTARUm2O/ALYDawVZ7GDxccUlPJ0/gtYDPgPWBz4A9RklmxUUkfTA6DiEhTULIoIiIDKkqyjYDTwuTueRrfUWQ8zSqUxG4BzAB+CCTFRiQiIkOdkkURERkwUZKtgO8CogU4Jk/jPxccUlPL0/gf+Kq8DjgySrItCw5JRESGMCWLIiIyIEJfitcDE4GrgQOLjGeoyNP4auBgwICLoiRbqdiIRERkqFKyKCIidRcaYLkUWBZ4BNgxT+P2YqMaUo4CLgPmBq6JkmzeguMREZEhSMmiiIgMhCOADYG3gW/maTy14HiGlDyNHbAr8Cg+IVcLqc1h8zCIiDQF9bMoIiJ1FSXZt4ErgTZgwzyN7yo4pCErSrLP4PteXBA4Nk/j/QsOSUREhhAliyIiUjehQZsH8dUj98nT+ISCQxryoiTbALgD34jQt/I0vrbgkKQLUZLtCZCn8elFxyIiUgtVQxURkbqIkmwufIni3PgWUH9fbETDQ57GdwMHhMnzoiRbush4pFvfC4OISFNQsigiIv0WOog/C1gJ+C/ww/BcnQyO3wHX4VuevSxKstHFhiMiIkOBkkUREamHXfD9/00FvpOn8ccFxzOshJZmfwDkwFqAqv+KiEi/KVkUEZF+iZJsReDUMLlHnsZPFRnPcJWn8QfANsAsYM8oybYtOCQREWlyShZFRKTPoiQbC/wFGAtckKfxBQWHNKzlafwQ8IsweVaUZFGB4YiISJNTsigiIv1xPPAF4Flgr4JjEe8M4BpgHuBC9b/YOPI0npSn8aSi4xARqZWSRRER6ZPQn+KewGxgOz2n2BhCw0I/At4A1gMOLDYiERFpVupnUUREei1KskWBx4H5gJ/naXxSwSFJhSjJNgJuBdqA9fM0vr/gkIa9KMn2BcjT+PiiYxERqYVKFkVEpFdCNxln4xPFm4GTi41IqsnT+DbgOKAFuDhKsgkFhySwRRhERJqCkkUREemtHwObAR8Au6o/xYZ2EPAvIEJJvYiI9JKSRRERqVmUZJ+low+/PfI0fr3IeKR7eRrPAnYAZgA7R0n2zYJDEhGRJqJkUUREahIlWQtwHjAe+EuexpcWHJLUIE/jp4EDwuRZUZLNX2Q8IiLSPJQsiohIrfbFt675Ouomo9mcDNwDLAycWnAsw9n0MIiINAW1hioiIj2KkuwLwENAK7BpnsY3FxyS9FKoQvwYMA7YJk/jywsOSUREGpxKFkVEpFtRkrXiq5+2AmcoUWxOeRo/D/wqTJ4RJdlCRcYjIiKNT8miiIj0ZF9gNSCnI9mQ5vQH4HZgAeAPoRsUGSRRkh0cJdnBRcchIlIrJYsiItKlKMk+BxwSJn+cp/HUIuOR/snTuB3YFfgY+DawXbERDTsbhkFEpCkoWRQRkaqiJBsBnA2MBs4OnbxLk8vT+GXgl2Hy5CjJFigyHhERaVxKFkVEpCt7AesCb+CrosrQcTbwN3x11N8VHIuIiDQoJYsiItJJlGQRcHSY3DNP4w+Li0bqLU9jB+wOzAR2jpJs44JDEhGRBqRkUUREPiU0enIWMB64LE/jq4uNSAZCnsbPAoeGyTOjJBtfYDjDxXthEBFpCiOLDkBERBrOzsDGwPvAzwqORQbW7/CN3KyKTxzV2u0AytN466JjEBHpDXPOFR2DiIg0iCjJ5geeBuYHfpCn8fkFhyQDLEqyLwL/CJNr52n8cJHxiIhI41A1VBERKXcMPlH8G3BBwbHIIMjT+EHgJPw1wZ+iJGstOKQhK0qyo6MkO7rnNUVEGoOSRRERASBKsq8APwRmAXuERlBkeDgYyIHVgL0LjWRo+3IYRESagpJFEREhlCb9IUwek6fx00XGI4MrT+OpwJ5h8tAoyZYoMh4REWkMShZFRATgF8DKwPN0dJkhw0iexjcCV+FbwT2h4HBERKQBKFkUERnmoiRbCjgkTO6Vp/H0IuORQv0cmAZsEyXZJgXHIiIiBVOyKCIiJwPj8H0q3lx0MFKcPI1fBg4Lk6dGSTamyHiGoFfDICLSFNTPoojIMBYl2beAbwIf46uiipwITAZWxPe7eESRwQwleRrvWHQMIiK9oX4WRUSGqSjJ5gKeBJYEfpan8SkFhyQNIkqySfjuU2YCK+dp/HyxEYmISBFUDVVEZPg6EJ8o/gs4veBYpIHkaXwncBEwGjg5SjIrNqKhIUqyE6MkO7HoOEREaqVkUURkGIqSbFlgnzC5V57GbUXGIw1pX2AKsDnwrYJjGSpWC4OISFNQsigiMjydAIwCzsvT+B9FByONJ0/jN4GDwuTJUZKNKzIeEREZfEoWRUSGmSjJNgO2xDdqc0DB4UhjOwN4FF9def9iQxERkcGmZFFEZBiJkmwUvrVLgMPzNH6jwHCkweVpPAf4WZjcL/TJKSIiw4SSRRGR4WVvYHngaXz/iiLdytP4HuAvwBjg+ILDaXbPhEFEpCkoWRQRGSaiJFsU+E2Y/HmexrOKjEeayn7AdOC7UZJ9rehgmlWexrvlabxb0XE0MjM718ycmUVVlpmZ/TEsv9vM5uphW3ea2YyKeS1mtnTZdBS294e6vYlP7y83s6cGYts17v8VM3vfzDq1aGxmSXjvn5jZqCrL9w/Lt6ljPJ/6/KXxKVkUERk+UmAu4No8jW8qOhhpHnkavwIcHSZPipJsZJHxSG3MbEkz2zEkWEOhCvGpwI+Ae4DNnXOf9LD+kcAupQkzWxx4BPhB2TrvADsB59Q31IbxN2BeYMUqy74BzAbGA+tVWf4VoB24ox6BdPH5S4NTsigiMgxESfZlYGd8J+u/LDgcaU7HAzmwCqDSsT6IkuysKMnOGqjtlyWHF5nZm/gqr6fjk6FqyULTMLMTgD2Bu4DNakgUcc7d6py7pGzWkvjvb/k6U51zFzrn/lnXgBtHKdH7cvlMMxsHrAucBzhgk4rlFpY/6px7r06xdPr8pfEpWRQRGeKiJGsBTgmTx+dp/HyR8UhzytN4Or7vRYAjoiSbr8h4mtTyYaiLbpLDHYCF8c+Zzg3M6GYzDc/MjgZ+gU8UY+fc1IJDaia3h/G6FfMnAaPxzyM/hi9lLLcyMB9w60AGJ41PyaKIyNC3C7Am8BodVQlF+uJKfLW2+YDDC45l2OlFcjhkmNlhQIL/3m1emSiWPXN4gJldY2YzzexVM1u8/JlFM5sM3B9edkh4zaRqzyya2SJmdn543nCmmb1sZn8ws4Uq9j3azA4xs6fMbHpY/xQzW6DK+9jYzO4P671jZn/uYr1dzexfYb0PzOw6M1u9Yp1zzexdM9vazF43s2khoe7EOfcK8DwVJYv45HA68HfgNmA1M1u4bPlXwvi2sv2OM7Mjzez58Lm8ZmZnVryu9Jzm5WHdj8P72Lva518tZmksShZFRIawKMnmwT+3A/CrPI11R176LE9jh29Rtx3YI0oyVSkbQMMxOSxnZgfiG+V6EtjCOTetm9UPxH8WPwXOcc69VrH8buDQ8PdV+Kq5/62yz5HAzUAM/Blf9fVK4IfATaWGYsysBV/qdijwb3z1/svxVbRvMbMxZZtdKuzzfvzv53ZgMvDXin2fCJwNvAzsA5wArArcZ2ZfrQh1nrDuqcBhQHfPod8BfM7M5i2b9w3gHufczPA+DNi4bPn6+BLpv4fYxoTt7Bv29TPgUvzn+EBlIo2v1roDvn/WP4btHBqWdfn5S+PRA+oiIkNbAiwE3IevbiTSL3ka/ydKsjOAvYAToyTbKCSR0k9mtiTwVWAzYENgAr4BkvKEcEyVl9ZiKTNbqX8RDoh24BnnXHvF/F/iEz+Hr7q7CvBAN9uZBXzHOfdhtYXOuRfM7GZ8wvKYc+5C8CWTFauuDnwB+JVz7n9dxZjZB8C3gCWAV/DPgK8PHOicO7psvZfw3RJ9Gyg9LzkG+KZz7rowfZaZLQpMMrOFnXNvmdmX8Ynk0c65A8u2dyq+muiZZraic670W2sFTnDOHdXNZ1JyB/BjYB3gRjNbAv8M69lh+d3459m/AVwY5n0F+LtzrlSF+RfAl4BNnXM3l8V3Kf78cgSwe9k+58JXGb67bN1WKj5/aXxKFkVEhqjQgXqpMZtf6oJe6ug3+FKDr+NLYK4vNpym8Wj5xAAnh+VGA8fWYTsDYSywJb40r9xP8VUgjwduAC42s9Wccx93sZ17u0oUe+l1fAK7p5m9AtzonJvinDsMX4JX8m1gDp37q/0TPnl6umzeR3T+jfwD2ABYDHgL2DbMv6JK9dTrgD3wCd6TZfNr/d2VGrlZF7iRjucTbwVwzk03s/uAjeB/38vP4EuxS7bFP8rwcEV8zwOP4z+P8mRxCr7VWmlyShZFRIauo/EXiRfnadzdHXmRXsnT+P0oyY7AV5M7Lkqym/M0nl10XI3upWO2OBLYxI7hIgY2Oaw0ZoC2Ww8fAZ36+MMnON8MicxJ+JKt0/AletW8VY9gnHOvmdnPgePwtTHmmNn9+ITtz865d8OqSwOvVj5D6ZybDjxcsdm3y0oES6aH8egwLjV89FA34S3Fp5PFmt6zc+5tM3uCjkZuNgmv/U/ZarcCXzOzZYG1w7zbypYvj0/s3+lqP2Y2Nrx/qP6epQkpWRQRGYKiJFsH2B7/zMkBBYcjQ9Np+Oe5Pod/Tuu0YsNpCj/HVw0fga9eaTRuEle03coSjwOBTYGdzOwm59zFVdZvq9eOnXOnmNklwDfxidXX8VVO9zezLzvnnsVXA601GaqsYltNqR2RzfAlltX8u2K6N+/5DmByeNby68BNFcncbcBR+NLOLwLv4/tELI/vSXxV2a6U3zCq2/9DiqUGbkREhpgoyQxf4gNwQp7GLxcZjwxNeRrPwjdeAXBolGQTioynGSy1//VLLfHTi/+KTwh+j2/gYza+yl4tCcVQ1NLF/P8lG+G5uZ3xSdTpVZ4zrBszm2hmGwBznHPnOOe2xTcmtDcwPx1VLV8CljCzsRWvHxtaAv1+L3edh/HLzrnbygf892ME0F0DPz25A1+C/S1gATp3ifEwPkFcDVgPuL3iOdIc//7vqBLfKGCmc66rJFeamJJFEZGhZxt8M+lvA2nBscjQdhX+uaQF8KU/0r0lWsbNs4hz7ibn3D7OuZXwF+DbAicycMnjVOA9/DNnjTa8i28wplvOuYfwJV8TgItCCVlvlRLQ7l47Cd+f465l+24H/lmxjWvwpYu7Vbx+e2DrHvZRzRVh/JtSi6sAZjY//nd2CbWXZFZzJ/479fMwXV7FtPQe/4Y/d6xcuTzEtzDwk/KZZrYu/tnJWn7/tXz+0mBUDVVEZAiJkmwMcEyYPChP464agxDptzyNXZRkvwQeBH4eJdkf8jR+sei4mklosOWmMOxjZnPjS3Y2xpdALot/vm0u+n6Tfw6wo3Ouu+4VmsFvgS3wz94dTEdXDLUqPeO3lZnlwC1V1rkB+BdwtJktg2+UaEF8leuP8Q3YEMY7Ab83szXwjdqsgG+I5h46WkKtiXPuVjO7ENgRWNTMrsQno7sDiwKTe+g6pKftf2hmj+Cr0z7unHu9ymq3AqX+JiuTxWOArYBTQ8ut9+IbwdkL/9zpfjWE0enzD/1ASgNTyaKIyNCyNxDhGy44p9hQZDjI0/ghfHP7o/CNKkk/OOc+LqDksSk452bjq6POBA4ys/V6+fqX8QnnYvj+Cb9eZZ1Z+Ocj/wBsHtb7Jb710nXD84ql9TbCJ1Hr41tF/SZwEr7LiL40+PQDfCuw8+BrhRwAvAps7pw7vw/bq3R7GFdWQaVi/ovOuRfKFzjnpuBvYvwujE8K8d6I/1zKG8upqpbPXxqPqaEiEZGhIUqyhYDn8M+lfCNP464uCETqKkqyJfEdxo8B1s3T+P6CQ2pIUZLdCZCn8aS+bqOPJY8fAdsNgZJFERlkKlkUERk6DsMnijcoUZTBlKfxK5Q1qhQaWZLO7g9Dn6nkUUQGk0oWRUSGgCjJVgYewzeA8IU8jZ/s4SUidRUl2dz4ku2FgG3zNL6s4JCGpS5KHg3YwjlX2fG9iEi3VLIoIjI0HI8/pp+pRFGKEBpTOjhMpqGxJRlkXZQ8bgLcXXBoItKElCyKiDS5KMk2xDfIMIXetw4oUk/nAI8DS+Mb6pAyUZJdESXZFT2vWT8hebyjrIN7EZGaKVkUEWli4dmwUl+Kx+Rp/E6R8cjwlqfxHGDfMPnrKMnmLzKeBjR/GEREmoKSRRGR5vZdYC3gTXxT5iKFytP4Znz/dROAXxccjoiI9IOSRRGRJhUlWStwZJg8LE/jqUXGI1Jmf3xjS3tFSRYVHIuIiPSRkkURkea1K7Ac8CxwdsGxiPxPnsaPAhcBo/CdcIuISBNSsigi0oSiJBtPR2M2B+VpPLvAcESqORiYBXw/SrLViw6mQdweBhGRpqBkUUSkOe0NLAI8BFxecCwineRpnAOnhsljCgylYeRpfESexkcUHYeISK2ULIqINJnQwuT+YTLJ07i9yHhEunEU8BGwcZRkGxcdjIiI9I6SRRGR5nMAMA9wa57GqtImDStP4/co69olSrJhfd0RJdmNUZLdWHQcIiK1GtYHbRGRZhMl2WeA/wuTSZGxiNToJOA1YHVgu4JjKdrYMIiINAUliyIizeVQYDRwaZ7G/yo4FpEe5Wk8HfhNmDwySrLRRcYjIiK1U7IoItIkoiRbCfgBMAc4qOBwRHrjPOAJIAL2KDYUERGplZJFEZHmcRT+uP3HPI2fKzoYkVrladxGR7Xpg6Ikm1BkPCIiUhsliyIiTSBKsnWBbwHTgMMLDkekLzLgHmB+YL+CYynK9WEQEWkK5pwrOgYREelGlGQG3AWsDxyZp7GqoEpTipJsHeB+YDqwXJ7GrxUckoiIdEMliyIijW9zfKL4HnBcwbEMOjNbwcz2NrMLzewpM2s3M2dm3y06NumdPI3/AVyBbxH00GKjERGRnihZFBFpYFGStdDRT92ReRp/VGQ8BdkDOBH4PrACYIVGI/11INAG7BoabRo2oiS7M0qyO4uOQ0SkVkoWRUQa2/eBzwMvA2cUHEtRHseXqG4LLIuvkitNKk/jZ4Cz8NcgRxccjoiIdEPJoohIgwr90ZUas/lNnsYzioynKM65Pznn9nPOXeace77oeKQuDgemAt+Mkmy9ooMREZHqlCyKiDSuPYCl8CVrFxYci9TAzFY2s3PN7DUzmx6esdw7LDMze8TMXjWzMUXHWqQ8jd8ETgiTx4RGnEREpMGMLDoAERHpLEqyeYBfh8kDQz910sDM7P/wCVA78DdgDrAJcKKZvY5/Tm81YHfn3LAsJa5wPP6GyHrAFsB1xYYjIiKVVLIoItKY9gUWAO5F/bI1PDPbATgF+ABYwzm3mXNuS+CHYZWt8K1/PgecU0SMjSZP4ynAb8Pk0aExp6HusjCIiDQFlSyKiDSYKMkWBn4ZJvfP01gd4jYwMxuLb60V4P+cc0+WLb4qjL8DjAG+75ybM4jhNbo/AD8HVgZ2As4tMpiBlqfx6UXHICLSGypZFBFpPAcD44Hr8jS+t+hghgozOzY8Q9jbYfEeNr01sCDwoHPur+ULnHOf4KuljgH+A/xlQN5ck8rTeCb++w5weJRkQ/pZzijJxkVJNq7oOEREaqWSRRGRBhIl2WeB3QGH749O6mcxfD+NvdXaw/LNw/ivXSwv3Zg9yDnX3of9D3UX46tdrwrsBfyu2HAG1A1hPKnIIEREaqWSRRGRxnIE/kbeeXkaP150MEOJc25H55z1Ych72PQXw/juygVmNiH8+Zhz7tp6vp+hIk/jduCAMPnrKMkmFhiOiIiUUbIoItIgoiRbA9gemAkcUnA4Urslw/j1KssOC+NXBimWZnUTcCcwL7BfsaGIiEiJkkURkcZxdBiflqfxy4VGIr1RaoBovvKZZrY6vlol+G4zpAuhEackTP48SrLFioxHREQ8JYsiIg0gSrKvA98ApgBHFRyO9M4TYVxKDDGzxfCN2ZQSyc+amTqe70aexg8AVwJjUcm6iEhDULIoIlKwKMkMSMPksXkav1dkPI3GzNYws3+UBmCNsOioivlF+X0Y/9jM/mlmfwX+CyyL72fxJXzXELeZ2bYFxdgsDsSXwv4wSrK+NEbU6M5liHcPIiJDi1pDFREp3tb4RlLepKO/PukwD/ClKvOXG+xAqnHOXWRmI/D9BX4+DM8CBzjnbjCzV4CzgK8DlxQWaBPI0/jpKMnOAX4MHAl8t+CQ6ipP43OLjkFEpDfMOfX1LCJSlCjJRuKrMS4P7Jmn8RkFhyRSqCjJFscn22OBdUL11CEhSrIFAPI0frfoWEREaqFqqCIixdoVnyg+B/yp4FhECpen8WvASWHymFBNe6i4PAwiIk1ByaKISEGiJBsHHBomD8rTeHaB4Yg0kmOAD4CvApsWHIuIyLClZFFEpDg/AxYFHgb+WnAsIg0jT+MP6WgV+OgoyXS9IiJSAB18RUQKECXZfHT0K5fkadxeZDwiDehU4BVgVWD7gmMRERmWlCyKiBQjASYAt+VpfFvRwYg0mjyNZ9DR3+JvoyQbXWQ8IiLDkZJFEZFBFiXZkvgqqNBRuiginZ0PPAlEwO7FhlIXZ4RBRKQpqOsMEZFBFiXZ2fhWUC/L01idtIt0I0qybwLXAO8Cn83TeErBIYmIDBsqWRQRGURRkq0ETAbmAAcVG41IU7gOuBdYANin4Fj6JUqyJUPNAhGRpqBkUURkcB2JP/b+KU/jZ4sORqTR5Wns6KiuvU+UZAsXGU8/XRAGEZGmoGRRRGSQREn2ZWArYBpweLHRiDSPPI3/ji9hHA8cXHA4IiLDhpJFEZFBECWZAWmYPDFP4zeKjEekCR0ItAO7R0m2bNHBiIgMB0oWRUQGx2bABsD7wLEFxyLSdPI0fhzfOupI4IiCwxERGRaULIqIDLAoyUYAR4fJI/M0/qjIeESa2CHATGC7KMnWLDoYEZGhTsmiiMjA2wH4AvAKcHrBsYg0rTyNXwZODZNHd7dug/pdGEREmoL6WRQRGUBRko0GnsJ3Kr5LnsbnFhqQSJOLkmx+4HlgArBxnsa3FRySiMiQpZJFEZGB9RN8ovgEajJfpN/yNH4POCZMpqGad1OIkmyFKMlWKDoOEZFaNc0BVkSk2URJNg9wUJg8ME/jtiLjERlCTgLeANYEtik4lt44MwwiIk1ByaKIyMDZB1gAuBffR5yI1EGextOAQ8PkkVGStRYYjojIkKVkUURkAERJtjA+WQRI8jTWA+Ii9XUO8AzwWeDHBcciIjIkKVkUERkYBwHjgevzNP570cGIDDV5Gs8BDgyTv4mSbK4i4xERGYqULIqI1FmUZMsAuwOOjotZEam/K4F/AgsDPy82FBGRoUfJoohI/R0BtAIX5Gn8n6KDERmqQvXu/cPkflGSLVhkPDX4bRhERJqC+lkUEamjKMnWAB4GZgLLh07ERWQARUl2I7ApcGKexr8oOh4RkaFCJYsiIvWVhvGpShRFBk2Cr/a9Z5RkUcGxdClKstWiJFut6DhERGqlZFFEpE6iJNsY2Bj4CDi64HBEho08jf8NXAyMAg4vOJzunBgGEZGmoGRRRKQOoiQbQUepYpqn8XtFxiMyDB0MzAZ2jJLsC0UHIyIyFChZFBGpj+8BawCvAScXHIvIsJOn8YvAGYChkn0RkbpQsigi0k9Rko0CjgyTh+RpPK3IeESGsSOBT4DNoyT7atHBiIg0OyWLIiL9tzuwDPBf4LyCYxEZtvI0fhs4LkweEyWZFRmPiEizU7IoItIPUZLNA/wmTB6Qp/GcIuMREU4A3ga+BHy74FgqHRgGEZGmoGRRRKR/9gEWAO4Dri04FpFhL0/jT+hoEfWoKMlGFhlPuTyN78vT+L6i4xARqZWSRRGRPoqSbBF8sgiwX57Grsh4ROR//gi8AKwA7FJwLP8TJdm6UZKtW3QcIiK1UrIoItJ3BwPjgWvyNL636GBExMvTeBbw6zB5aJRk44qMp8xRYRARaQpKFkVE+iBKsuWA3YB29AySSCO6DHgEWAz4WcGxiIg0JSWLIiJ9cyQwEvhznsZPFh2MiHxansbtwP5hMomSbL4i4xERaUZKFkVEeilKsrWBbYAZwKHFRiMiXcnT+FbgdmACcEDB4YiINB0liyIivRD6bTsmTJ6Up/GrRcYjIj1KwvinUZItWWgkIiJNRsmiiEjvbAJMAj6gI2kUkQaVp/FD+OcXR1N8TYCfh0FEpCmYc2rpXUSkFlGStQD/Ar4A7Jun8e8KDklEahAapHoSf5N8FT1nLCJSG5UsiojUbkd8ovgKcFrBsYhIjfI0fhbf9+IICuy6IkqyjaIk26io/YuI9JaSRRGRGoR+2o4MkwflaTyjyHhEpNcOB6YB34qSbL2CYjgoDCIiTUHJoohIbX4BLI7vt+3CgmMRkV7K0/hN4IQwmYbGqkREpBtKFkVEehAl2cJ0tKi4b+i/TUSaz3HAe8BXgC0KjkVEpOEpWRQR6dmhwFzA9Xka31FwLCLSR3kaTwF+GyaPDo1WiYhIF5Qsioh0I0qylYAfA23AfgWHIyL9dwbwErAysFPBsYiINDQliyIi3TsWaAHOytP4v0UHIyL9k6fxTODgMHl4lGRjBnH3u4dBRKQpjCw6ABGRRhUl2YZADHxM8Z15i0j9XAz8ClgF2AsYlD5T8zR+ejD2IyJSLypZFBGpIkqyEcDxYTLN0/jtIuMRkfrJ07iNjkarDoySbOJg7DdKsi2jJNtyMPYlIlIPShZFRKrbEVgNeBU4sdBIRGQg3AjcDcwH/HqQ9rlPGEREmoKSRRGRClGSjQOODJO/ztN4WpHxiEj95WnsgH3D5M+iJPtskfGIiDQiJYsiIp39HFgCeBS4sNBIRGTA5Gn8IHABMAo4puBwREQajpJFEZEyUZItDBwQJvfJ07i9yHhEZMAdCEwHto6SbIOigxERaSRKFkVEPu1QYC7g+jyN7yg4FhEZYHkav4rvIgfghNC4lYiIoGRRROR/oiRbCfgx0AbsV3A4IjJ4jgNeB9YEdhrA/ew0wNsXEakrc84VHYOISOGiJDN864ibAH/I03iPgkMSkUEUJdnOwHn4pHH5PI2nFhySiEjhVLIoIuJtjk8UPwJ+U3AsIjL4LgQeAhZjgGoWREm2bZRk2w7EtkVEBoKSRREZ9qIkGwWcECYPz9P4nSLjEZHBFxqz+mWY/FWUZEsMwG72CIOISFNQsigiAnsBywPPAKcWHIuIFCRP43uAy4GxwNEFhyMiUjgliyIyrEVJtiBwSJj8ZZ7Gs4qMR0QKtz8wC9gxSrK1iw5GRKRIShZFZLg7ApgA3AzcUHAsIlKwPI1fAE4MkyeExq9ERIYlJYsiMmxFSbYqHV1l/DJPYzUPLSIARwLvAOsB2xQci4hIYZQsisiwFEoLTsQfB0/L0/jJYiMSkUaRp/EU4KAweVyUZOPqtOnvhkFEpCmMLDoAEZGCfBuYBLwPHFZsKCLSgM7Gt1y6Gr4rjUP7u8E8jd/t7zZERAaTOadaVyIyvERJNgZ4Elga+L88jU8rOCQRaUBRkn0FuAeYAayYp3Hez+1NBsjT+Nz+xiYiMhhUDVVEhqNf4BPFJ4AzC45FRBpUnsZ/By4GxgDH12GTk8MgItIUlCyKyLASJdmiwK/D5M/zNJ5TZDwi0vD2A6YCW0dJtmHRwYiIDCYliyIy3BwNjAeuzdP4tqKDEZHGlqfxa/jWUQFOjpKstch4REQGk5JFERk2oiRbF/gBvsPtfQoOR0SaxwnA88BKwJ4FxyIiMmiULIrIsBAl2Uig1JDNcXkaP1dkPCLSPPI0ngn8PEweFiXZQgWGIyIyaJQsishw8RN8E/gvA0cVG4qINKEMuBGYQN+PIZuHQUSkKajrDBEZ8kIpwDP4i7zv5Gl8VcEhiUgTipJseeBxfD/VX8rT+MGCQxIRGVAqWRSR4SDFJ4o3A1cXG4qINKs8jZ8Bfg8YcEqUZL26joqSbM8oyfTMo4g0DSWLIjKkRUn2ZWAXYDbwszyNVZ1CRPrjt8AbwJfwx5be+F4YRESagpJFERmyoiRr4dON2jxTZDwi0vzyNP6YjtaUj42SbIEi4xERGUhKFkVkKNsdWB14BTVqIyL18xfgdmA+fDV3EZEhScmiiAxJUZItSEdH2r/I03hqkfGIyNARqrPvha/e/sPQh6uIyJCjZFFEhqqjgYnArcCVxYYiIkNNnsZPA8eGyTNCX64iIkOKus4QkSEnNGpzH/6u/yrhok5EpK6iJBsHPAFEwC/zNP59sRGJiNSXShZFZEiJkqwVOCtMHqdEUUQGSp7G04CfhsnDoyRbvMh4RETqTcmiiAw1vwA+D7yAb+JeRGTA5Gl8Pb7/1rnwfTB2KUqyfaMk23cw4hIRqQcliyIyZERJtjRwaJjcM0/j6QWGIyLDx97ANGCbKMk26Wa9LcIgItIUlCyKyJAQJZkBpwJjgb/kaXxzwSGJyDCRp/HLwGFh8tQoycYUGY+ISL0oWRSRoeK7wObAR/iqqCIig+lE4ElgWeCAYkMREakPJYsi0vSiJJsAnBQmkzyN3ywyHhEZfvI0ngXsESYPiJJspSLjERGpByWLIjIUHAksCvyDjpZQRUQGVZ7GdwN/BFqBP0ZJVnmdNT0MIiJNQf0sikhTi5JsbXyS2A6skafxYwWHJCLDWJRkE4H/AosAe+VpfHqxEYmI9J1KFkWkaZX1qWjA75QoikjR8jT+EPi/MJlGSbZEgeGIiPSLkkURaWb7AasCLwKHFxyLiEjJlfi+F+cGTgutNRMl2cFRkh1cZGAiIr2hZFFEmlKUZCsCvwmTP87TeGqR8YiIlORp7PCli1OAbwJbh0UbhkFEpCkoWRSRphMlWQtwNjAKODtP49sLDklE5FPyNH4NSMLkqVGSzVtkPCIifaFkUUSa0V7Al4E3gH0LjkVEpCtnAvcCCwPHFhyLiEivKVkUkaYSJdnSwNFhco/QmISISMPJ07gd+DEwC/gRMLHQgEREeknJoog0jdBIxFnAOODSPI2vKTgkEZFu5Wn8X+C3YXI54MPiohER6R0liyLSTHYBNgLeA35WcCwiIrVKgUfwN7peLzgWEZGamXOu6BhERHoUJdliwJPABGDHPI0vKjgkEZGaRUn2BZx7CLPWkW1zNnruuG+pYS4RaXgqWRSRhheqn56JTxQz4OJiIxIR6Z08jR8b4dofAGhxbRdGSTZ30TGJiPREyaKININdgC2Aj4CfhD7MRESajDF69qw5M0eOXmT8zGknFx2NiEhPlCyKSEOLkmwp4MQw+X95Gr9aYDgiIv3g3MKfvPdhS3tb+9TR4yYv+6trNio6IhGR7ihZFJGGFSXZCODPwNzAVYCeUxSRpjZmzqw5mz/197sAWtrbLlB1VBFpZEoWRaSR/R/wNeAdYHdVPxWRoeDYG0/6+2JT3n5rZuvoReaaOe2UouMREemKkkURaUhRkq0AHBMmd8vT+J0i4xER6a8Rzr02/7QPp46dM6v9tzeffmVLe1v7J6PH/WD5fa/aoujYRESqUdcZItJwoiQbCfwd+BJwQZ7GOxcckohI/5mNBU4DXgb4ZfyL9a78/IYbjZoz+4NZI1tX0E0xEWk0KlkUkUb0K3yi+Crws4JjEREZEOmNp9y39PuvvTxrZOu842ZNvyB0EyQi0jCULIpIQ4mSbDXgsDD5wzyNPywuGhGR+llun6uO/clWB3ypND2qfY478brjrxwze+asaaPGbjJ69szdioxPRKSSkkURaRhRko0HLgFagdPzNL6l4JBEROqmbcSIVV+Yb4n5yuet+uazH+360DXXA8xpGXlSlGTLFROdiEhnShZFpJGcAHwOeBJfFVVEZMjb9+4L/rPq608/0TaiZfSY2TMuj5KsteiYRERAyaKINIgoyb4D7AbMBLbP03hawSGJiAyKEThOu+aY6+eZ8cknM1rHfGHcrOmH9fwq6S0zm8/MjjOz3Mymm9mjZrZRWHaYmX1oZhMLDlOkoShZFJHCRUm2BPCnMLlfnsaPFRmPiMhgW2LK2zP2v+vcK8w5preO3v+z+127TtExDSVmtizwL2Av4DbgbGB54DIzWxTfr+8pzrkPCwtSpAEpWRSRQkVJ1gJcAMwL3Aiog2oRGZJaXPuzi015+6Ouln//0ZvySc8/eL+zESNGts25IkqyiYMY3pBlZiOBq4AlgK87537knPs/4CD8ueck/LPyvy8uSpHGpGRRRIq2HzAJeAuYnKexOn8VkSHp2eO//X/nXn7Yfd2tc8p1x92+2JS335rZOnoxdadRN98DPg+c7pz7R9n8h8N4G+A059z7gx6ZSINTsigihYmS7EvAEWFycp7GbxcZj4hI0eaaNb3thOtPuGz0nFmzp40au8XoObP2KjqmIWD7MD61Yv7MMJ6Gb2BNRCooWRSRQkRJNgG4GGgBfp+n8U0FhyQiMqCW2/eqUyd/95B1e1pvnVcef3+3B668FmD2iJEnhP5npe/WB15wzj3TxfIznHPvDGZAIs1CyaKIDLpQreocYBngUeCAQgMSERkEbTZiudfnWWhCLevu8/cLH1/npcceaR8xonX0nFlXR0k210DHNxSZ2YLABODpKos3CeMbBi8ikeaiZFFEivAz4DvAFGCbPI1n9rC+iMiwc8bVR9+48MfvvTtz5Kilxs6acY6eX+yTcWH8qefhzWwxYN8wOWdQIxJpIkoWRWRQhecUjw+Tu+Zp/FyR8YiINKp5Z3w8+5gbT7qsdc7sOdNHjdlm9JxZuxYdUxN6E5gNrBNKGUuto54DlEprFyooNpGGp2RRRAZNlGTzAZcBI4GT8jS+ouCQREQa2qQX//XO5IevywDmjGg5LUqylYuOqZk452bizzvzAfeZ2e+B+4GN6XgE4nAzU0NCIlUoWRSRQREl2QjgPOAzwD/xXWaIiAwbLe3t/17m/Vd73T3DAXf++dE1X33yP20jWkaPnjMri5JsnoGIbwjbE/gTMBHYK4y3cc6l+JouSwGbFhWcSCMz59SlmYgMvCjJ9gdS4ANgjTyN82IjEhEZZGZjgdOAl3v70vfGztO6+S4n//ituRdYcOzsGTdMbx2zhfqlFZGBppJFERlwUZJtBBwVJn+gRFFEpHfmnz5l9knXHf+XMbNnzpreOmbz0bNnHlh0TCIy9ClZFJEBFSXZ0sCl+OPNb/M0vq7gkERECrHsvlefs/12R27Q19ev88rj7+997yVXAswaOeqIZfa7bsP6RSci0pmSRREZMFGSjQOuxDcscANwaKEBiYgUqN1s8ffGTRzfn23s8cDlT2/y9H33ODMb4dqviJJsyXrFJyJSScmiiAyI0B/YWcBqwHPA9/M0bis0KBGRIeCUa4/923LvvPTinJaRE8bMnnldlGRjio6pEZhZq5n1KxkXkU9TsigiA2Vv4PvAVGCrPI0/LDYcEZGhYVT7HPenK4/468TpU6bMaB296pjZM/4cbtANd5cCr5rZZkUHIjJUKFkUkbqLkuxr+ObIwTdo80SR8YiIDDVLffjm9GNuPPmS1jmz58xoHbPd6DmzhnV3RGb2XWATfLcYl5vZ+WY2d7FRiTQ/JYsiUldRki0LXA60AEfnaXxFwSGJiDSEke1tD6z49gtv12t7mzz7jzd/ev+lVwLMbGk9epn9rtu8XttuJma2CHA2MC7MGgd8D7ipsKBEhgj1sygidRMl2bzA/cAKwPX46qd6TlFEBPrVz2J3/u+b+331+hU3mNTS3jatbUTLF/M0frKe229kZmbAbcD6QGvZoqnAns658wsJTGSIUMmiiNRFlGStwF/xieJjwA5KFEVEBt7J1x5316qvP/PfthEt40bNmX1zlGTzFx3TINoV+BKfThRnAX8HLigkIpEhRMmiiPRbaFjhFGBD4C1gyzyNPy42KhGRxvLZX11z8dbfP/br9d7uCBzn/vWQqxb76O23Zo1sXWLM7JnXRkk2qt77aTRmFgEnAZUtoE4HdnKqPifSb0oWRaQefgbsDszEVz2taxUrEZGhwMH8H48eP3ogtj3vjI9nn3nVkRfPPXPqtBmto9cdM3vmuUO5hVQzG4GvzVLZbcg04AfOuXcGPyqRoUfJooj0S5RkMXBCmJycp/E/ioxHRGS4WuWt56ccfdMpF/kWUkdvP2rOrCOKjmkA/QJYEd+YWslM4Hrn3DXFhCQy9ChZFJE+i5JsbeAy/LHksDyN/1JwSCIiw9oWT/399X3+fuFfzbW7WSNH/XrZX12za9Ex1ZuZrQgcTufqpx8Duw1+RCJDl5JFEemT0EVGhm+i/DzgsGIjEhERgJ88cMUzOz5y440AbSNGnLXMftdtXHRM9WJmrcAVwNiKRdOB7ZxzHw1+VCJDl5JFEem1KMkWBm4GFgjjH+dprIYERES60do252+rv/7U64OxryNuPePBjZ594H5nI1oMd3WUZF8YjP0Ogt8ASwHlz2NOBy5wzt1eTEgiQ5f6WRSRXomSbC7gb8BawMPApDyNPyk2KhGRJjBA/Sx2ZY6NsK13PG6bfy+2woqtbbPfmd3Sunaexvlg7HsgmNmawD10LlV8FVjBOTdt8KMSGdpUsigiNSvrS3Et4AUgVqIoItKYRrp2d8FlB1+59PuvvTK7pXXB1rbZd4aaIU3HzMbQdfXT7ypRFBkYShZFpCZRkrUA5wKbAu8Cm+Zp/FahQYmINJHP/uqaq7f4wYnfGMx9zjNz2pyL/3LgRYtOeeft2S2tS7XOmX1HlGQTBzOGOjkWWLBi3jTgFOfcAwXEIzIsKFkUkR6FvrpOB3YAPsGXKD5bbFQiIs3FwdhZLa0tPa9ZX4t+/N7MCy49+PwFpn7w4eyRrSuNmjPrpijJxg12HH1lZhsAP8Q3qFbigNeAgwsJSmSYULIoIt0KieJx+ObIZwBb5mn8z2KjEhGR3lj2/Ven/vGKI86dMP3jT2aNHPWlUXNmXR0eLWhoZjY3voumyuR2BrC1c27W4EclMnwoWRSRnhwM7APMAbbO0/jOYsMREZG+WP2NZz465dpjzxs3a/qMWSNHbTxqzqy/REk2sui4enAaMKFi3jTgt865/xQQj8iwomRRRLoUJdkv8P0ntgM75Gl8Q8EhiYhIP2yQP/LusTeedMHo2TNnzxo56juj5sy+MDyT3nDMLAa2BsaUzW4HngGOKSQokWFGyaKIVBUl2Z7ACWHyR3ka/7XIeEREmt3ottk3fPnlx14pOo4tnvr760fecvoFo+bMmjNrZOu2rW2zz2+0hNHM5gcuoHr10+8659oGPyqR4Uf9LIpIJ1GS/RQ4OUz+NE/jU4uMR0RkSBjkfhZ7cukqG3/m4G/sudOska0jW9tmXzC7pXVynsbtRccFYGbX4FvfHlU2eyqwn3Pu9GKiEhl+VLIoIp8SJdnedCSK/6dEUURkaNr2P7e+fOhtZ17U2ja7bXZL606tbbPPjpKs8GtDM9se2IhPJ4pzgH8BZxQSlMgwVfgBQUQaR3hG8cQwuWeexqcVGI6IyJCyzK+uufkbu562WdFxlNvh3zflh9x21kUj2+a0zW5pnRwSxsKqpJrZYsCZVK9+ur1TlTiRQaVkUUQAiJJsHzqeUfxJnsa6eysiMgzs+OiNLx58+x8vLksYLy6iWw0zM+BiYGzFoqnAT5xzrw12TCLDnZJFkWEuSjKLkuxQ4Pgwa7c8jc8sMCQRERlkP3gke+GIW8+4YPScWbNnt7R+b2TbnKujJBvT8yvrandgLaC8O49ZwJ34JFJEBpmSRZFhLDybcjJwCL458l3yNP5jsVGJiEgRtv/3zS8de8OJ542dNWPmnJaRm7e2zb4xSrLxg7FvM1sGf9Oycn/TgMmqfipSDCWLIsNUqGJ0PvB/+Du3383T+NxCgxIRkUJ96793v3bqtcecM/fMqdNnt7ROam2bfUeUZBMHcp9m1gL8lU/3pwg+UdzJOffuQO5fRLqmZFFkGIqSbCxwFfB94BNg8zyNryo2KhGRoW3MnFlXfP35B18sOo6ebPj8g2+feeWRZ0+cPuWT2S2ta7e2zb4vSrIlBnCX+wIrAOUN68wArnbOXT+A+xWRHqifRZFhJkqy+YBrgK8A7wGb5Wn8YLFRiYgMAw3Wz2JPHll0+Qm7feegye/MNd/ElrY5b7S1jPxGnsaP13MfZrYy8CCdG7V5G1jOOTelnvsTkd5RyaLIMBIl2WeB+/CJ4mvA+koURUQGx9FfnTx2yujxhXVL0Vurv/HMR5dftN9Z0fuvv97WMnLREe1t90VJNqle2zezUcCVdK5+Oh3YVomiSPGULIoME1GSfRn4B76qz2PAOnka/7fYqEREho8/rv3tq7/7/WO/UXQcvbHUh29Ov/qCX/75C28882z7iJa5zbXfsvT+121X6+vNbFkzuyj0n1jpMGAJwMrmTQfOdc7d2b/IRaQelCyKDANRkm0D3AEsANyEL1F8tdioRESkGUyc8cmcyy/c75JJzz/0kLMRrc5GXLL0ftcdGCWZ9fxqfgZ8D3jKzLYvzTSzLwJ7A+Mq1n8X2KduwYtIvyhZFBnCQh+K+wOX4av5nAlsmaexqvaIiEjNRrXPcedcflj2vcduuc2cw40YcWRLe9slocG0qsxsJLAzvt/EuYE/mtm1ZrYEcAWdn1OcDnzHOTd9oN6HiPSOkkWRISpKsnHARUAaZu0H7JGn8ZziohIRkWY1AsexN5587353nfuX0XNmzWkb0bJtS9uce6MkW7yLl3yDT19rjg/zXsTXdCk3DTjROfdQ/SMXkb5SsigyBEVJthRwL7A9vmuM7+RpfFyexmr+WERE+mWPB654+oyrjvrjfNM++ritZeTqLe1t/4qSbO0qq+6JL1EsNxpf0lhequiAV4BDBiZiEekrJYsiQ0yUZF8DHgJWA57DN2SjPhRFRAo2bvbMC+Kn7nm26Djq4esvPPT2FRf+6g+ffe+V19pGtCxkrv2epfe/btfScjObF9iwxs3NwFc/nT0gwYpIn6mfRZEhIjQ08HPgOHzHxjcBO+Rp/EGRcYmISNBk/SzWYmrrmJbdv/3r+O9Lr746wIj2tnPbR7Ts9dIxW+wMHI+vetqT6cCfgP2cczMGMFwR6SWVLIoMAVGSzQdcDZyATxRTYAsliiIijWOX7x4y/6vzLDi66DjqafzsGW0XXnbwtT/5x+XXtrbNbmsf0TK5pb3tn7S0/pLaEkXwVVJ/hG8xdc2Bi1ZEeksliyJNLvSf+BfgM8CHwK6qdioi0niW2e/au5d979XlbjlnrzOLjmUg3Lrs2gsfuMlPt3991rQJb5zzU1zbrL5sZjq+RPIQp4tUkcKNLDoAEembKMlG4PuiOgr/W/4nsG2exnmRcYmIyPC08XP/fGuVN/c+Y93FV9zdubZ5+7iZ0cBewLH4BtpEpECqhirShEIz5TfgT6Yj8dVP11eiKCIiRVrgk/dnvfX0vaNpb+vLy2fhW0Vd3TmnRFGkAahkUaTJREm2HXA6MC/wPjA5T+Prio1KREQE/gjRnL5dX04H/gts7Jx7v85hiUgfKVkUaRKhEZvTgO3CrBuAH+Vp/EZxUYmIiHT4E6w1C0b18mXTgL8B31VrqCKNRdVQRZpAlGRbAP/BJ4pTgd3xrZ0qURQRaRJzzZp+1ncfv+2pouMYKG/BqMdg+V6+bBpwPvBNJYoijUetoYo0sCjJFgFOAr4XZt0H7Jyn8fPFRSUiIn0yBPtZLPcrWPVk2LzmksWW1vaRExf5/ex3X953gEMTkT5SsijSgKIkM2BXfPPhE/F3Xg8CTs7TuE+tBoiISLG22vmEZY+58aQjV3j35f8WHctAWBJ2exUWrWVdGzmK+Tb7GXOt+NU5wBGYHZunsUoWRRqMqqGKNJgoyVYC7gD+hE8UbwJWztP490oURUSa12OLLHvOT7+5/wZFxzEQ7oeJb8KCtaw7CmYd19J68aZjJ/wHs5GYHTaivf2JKMk2Heg4RaR31MCNSIOIkmwicAjwU6AFeAfYG/hLnsaqAiAiIg3rBFjNgXW3jkH7WJhxGZwXz5z6Npcd/OzFq27yr5PW2/5bb829wDLAjUvvf/1VzuwXeRq/NEihi0g3VA1VpGBRkrUAuwBH4e/KOuBM4KA8jd8rMjYREamfZfa79u5l33t1uVvO2evMomOpp3ZgIuzzMczV1Tot0DYBptwC564JU8qXTW0d03L4hj9e76qVv7b+rJGjRpprn+FsxFHA7/I0njbA4YtIN1QNVaRAUZJ9DXgA+CM+UbwHWCNP4z2UKIqISDM4H5ac2U2jNiNhzuLw5qNwZmWiCDB+9oy2Y2465e4rLvzVKWu++uSzzkaMAQ431/5clGS7hJuqIlIAJYsiBYiSbPUoyW7CP5u4JvAasD3w1TyNHy0yNhERkd44E9aaDa3VlrXC7JXg+f/An5eEmd1tZ5W3np9yxUX7XXzUTaeev+SHb77rbMSiwDnm2h+JkuwbAxK8iHRL1VBFBlGUZMsARwA7hFkfA8cAJ+ZpPLWwwEREZMCttvclW+9z9wU/2enRG+8tOpZ6eR9GLgL7VUsWW2H21+BfGdw80j9iUbM5NsJO/Mr3V7totU03/GDchPEA5trvcDbiN3kaD5nPT6TRKVkUGQRRki0LHADsjG9Yaha+r62j8jR+t8jYRERkkAzBfhYPhs8fC1tW9q3YCrN3hjv+BP/oz/Y/HDPXyCO/9sOvXLfiBuvOaB3dCmDO3eLMDsnTuF/bFpGeKVkUGUBRkq0A/Br4Pr7adztwIfAbtfQmIjK8bPSjM75wzI0n/2bN1596vOhY6mUZ2PVFWLJ8XivM/jVcfQg8Wa/9vDrPQmOOmfSDr96y7DprzuxIGm90Zr/N0/i+eu1HRD5NyaLIAIiS7IvAPsD38E2JtwHnA0fnafxskbGJiEgxhlprqI/C3GvB3m2+uyfA96H4B7holwEqPX1p4iJjj9tg50m3LLfOGrNGjhoJYM7d58yOBa7L07h9IPYrMlypn0WROgmttX0T+CXwlTB7NvBnIM3T+MWiYhMREam338EXLDyLOML3oTj9Cjh3ExiwxyuW+vDN6adee+yNL8672F0nrL/jV2//7BdXmzZq7LrA1eban4mS7HjggjyNZwxUDCLDiUoWRfopSrK58f0k7g0sE2Z/BJwFnJKn8StFxSYiIo1jKJUstgPzw88/hAktMGdemHI7/PkL8MlgxvHOuImjTl5vu3Wyz62/9vsdDeG842zEWcBZeRoPmedDRYqgZFGkD6IkM2AtYDd8lxfjw6IXgBOBc/M0/riY6EREpBENpWTxr7DoDrAr4JaEN++BixbvoWuMgTSzpXXE6etss+qVn//6eq9MXGR+AJxrBzLMzgBuVhVVkd5TsijSC1GSTcA3VvNjYLWyRXfjk8Rr8zRuG/zIRESk0Q2lZHESbHEXrLkmPHEnXDWXfza/cO0YV6yyYXT55zf8ykNLrLR024iWEQDmXO7M/oivoqoaPyI1UrIo0oMoyVqBTfB9I24FjA2L3gPOBf6Up/FThQQnIiJNY82fXrT5gX8752dbP3FH03f5MBfsOwn+fS3cOqLoYLrw3HxLjP/j2t/+8q3LfmnV98dPnAsAf+H7N8zOB65ULSCR7ilZFKkiSrIRwLr4BPF7wPxli+/AP494dZ7GhVW5ERGRJjOE+ll8COZZC6YUHUctZo0YaResEa9w0/Lrrv3IYit8Zk7LSN96q3PTMLsKuAS4Ted0kc6ULIoEUZKNBNbHlx5uBXymbPETwEXAJXka54Mdm4iINL/1f3L2l466+dQD1s8ffbToWIar1+ZZcMx5a2yxxt8++8UvPLvAZxb+3wLnpmB2HXAFcFOextMLC1KkgShZlGEtSrJxwMbAt4EtgfnKFr8KXIxPEv+Tp7F+LCIi0mdD6ZnFoeDBxVec99JVN1n7/s+ssvxrExbuOP87NxWzG4AMnzi+VViQIgVTsijDSmjFdBX8M4ib4EsSR5Wt8gxwVRgeVMtpIiJSL0oWG9cDS648/9UrTVrjvqVWXf6leRdb4FMLnftXSB5vBB5QQ3YynChZlCEvSrIlgK8C3wjDImWLHfAQcHUY/qsSRBERGQhKFpvDvxdZbsLVK09a7aHFV1r2vwstvej/nnEEcO4DzO4A7gzDk7qxLEPZyKIDEKmnUHK4PL7EcIMwjipWewO4GbgFuDVP43cHM0YRERFpXKu++exHq7757F3AXR+OmWvkNSt9dYV7l1ptpUcW+9wS78w177zA1mEA596LkuwuoDQ8rpJHGUpUsihNLUqyBYE1gS8CawHrAAtVrDYFuBffiunN+AO5vvgiIjKoVLLY/B5YcuX5/7bMF1f896LLRU8utMyiH42de9ynVvDPOz4EPFAa8jR+rYhYRepByaI0hVBiuAj+ecM18InhWsBSVVZ/C7gnDHfjG6fRXT4RESnUOnudN+mQ287cd7Nn7n+o6Fik/9oxHl5ixQXuWGatFR5bdPml/7vQ0gu/P27CXJ1WdO41zB4GHgP+HcbP69pEmoGSRWk4UZLNB6wMfL5imK/K6tOAfwEP4p89fBB4TiWHIiLScIZQP4tS3XPzLTH+7qXXWPbxRZZd6qkFo4VfmG+xBWa0jhnVaUXfx+N/8Injf4Cnw/CKnoGURqJkUQoREsLlgGXLxqW/qyWFAB8Cj+PvypWSw6d0Z05ERJqBShaHnzk2wv7xmVUWfGSxFaLn5l9ysRfmW2L+VyYuPO+HY+cZX/UFzk3H7Fk6ksengReAHHhTiaQMNiWLUndRkrUCiwNLhuEzZX8via86Om83m5gKPIlPDJ8I48eB11ViKCIizUrPLErJSxMXGffAkp//zH8XWnrxfN7FFnp1wkLzvDnXAhM+HjN+bJcvcm4WZi/hE8cXwzgHXgNex18nTRvw4GVYUWuoUpMoyVqA+YGFaxgWBayHTU4FngWeqzJ+U0mhiIiIDFVLffjmtKU+fPMp4Kny+a/NveCYRxdbfrFnFlhq0ZcnLrLgKxMXnvD2+Pnmem/chLmmjh43Bl8Da7muthvtf/1HmL2Ob/n99TC8AbwNvFs+KLGUWihZHCaiJBsFzFUxzIMv4asc5qsybwI9J4AlDn9wegX/XMYrFX+/DLythFBERESkw+IfvzNj8affeSF++t4XKpe9O27iqCcXWnqhF+ZbfIHXJiw0/xtzLzDxzbnnn+v9sRPGfjh27vEfjR4/rq1l5AT8NduKPe0r2v/66ZiVJ5DvAR/VOEzRY0DDg5LFQRJK5kYCrd2MRwFjqgyju5hfPowFxgNz0zkpnDtsv7/ex7c0WhrerpguDa/naTy7DvsTEREREWCBaR/O2iB/5NUN8kderba8HeOViQvP9eK8i8/7+jwLzvvm3PNPeGf8xHneGzdx/Edj5ho9Zcz4MVNGjx/zyahxY6aOGjt6TsvIsXQ8ItRr0f7Xz8BsKr622LQaxzMrhlld/N3VsllAG9CuQofB0bTJYpRkSwN7AyN6GKyGdWoZKrdTSv56SgBL41pL5QZKG/BxGD4pGz7oYni/YvqjPI3nDH7YIiIiItKTETiW+vDNT5b68M1P8DW5utSO8f64eUa/OmHhCW/ONf/c746fONcHY+eZ6+PR48ZMHTV2zCejxo35ZPTYkZ+MGjdqWuuY1mmjxoya1jpm1PTW0aNmjBw9akbr6FbMSgUW8w/KG6wQJdkcYA7+GndOxdCbee34WnHtVf6u17Ir8jS+Z4A+igHVbQM3UZLdOXih9No801/69+rTnryL+Tb9KWZF52I1cVWG9ip/t/dxaKPjh9BWMejui4iISEFmvv7U+PdvOeNziy+9hi270qSPi45HpD8c4MzMmY1w2Ih2/7eV/T3CYdZuI8yZWXsYHIYzw5lZOyPK/gZnI3BGaZ2OsRkOStv3ATTHdT/TX3iY2e+/xsQvfOOF9lFjuk3gi5Sn8aSuljVtySIwY9Ybz7z7yWO3LNAy9wLvTfzKDu+H+a7O457WKU/2uksGRUREZBhqn/FJyzvXHLtS2yfvjX35w7faJq6xxQs2oqXosEQGnQHmHDhHC/3qBcQAM5yV/u5qcD61NAcWsszSfAjLStt0Hdsu348fG/6K3ih7if+j+uuM9x+4Yu4Z77/WMu9qm03pz5stUlN3nWG+OPEvwHeBrzvn7io4JBEREZH/CdcqFwLbjVp0uQtmvfHsD4CNnXO3FRyaiAwwM/sisLBz7vqiY+mrEUUH0B/OZ7o/wne5cKmZLVpwSCIiIiLllgQ2Aw5ZeLujlrHWMW3ADgXHJCKDwDn3YDMnitDkySKAc+5jYGt8i5+7FRyOiIiIyP84514GVgGOGjFqbPuYaLV3gK3NNw4iIkOUme1rZl8qOo7+avpkEcA59wTwReDwomMRERERMbOFzOynZmbOudecc+0A41f+2tvAS8Bnio1QRAaKmS0OHAtsWnQs/TUkkkUA59yTzjlnZkub2deLjkdERESGJzMbCVyKv1j8bPmyccuv+4Fz7gvOuWcKCU5EBsP38Q3eXFJ0IP01ZJLFMn8ArjSzFYoORERERIalY4BJwG7OuefKF5S6+jKzcWY2dvBDE5GBFBq1+gFw/1C4KTQUk8XdgNnAtWY2b9HBiIiIyPBhZtsDvwROcc5dULF4d2B3M4uAt1BDNyJD0RrASsB5RQdSD03ddUZXzGx94HbgLmAz59ycgkMSERGRIS7cpM6Bx4ANnXOzuljPgKeBN5xzXx28CEVkoJnZ1sCJwCrOuQ+Ljab/hmLJIs65e4A9gI3wd/dEREREBpRz7gPgO8DW1RLFKMm2jJJsy9D119nABmb2ucGOU0QGjnPuCmCpoZAowhBNFgGcc2cDOwOnFR2LiIiIDF1mNq+ZbQrgnLvdOfd2F6vuEwaAP+Mfm1G3XyJDhJktbGYjSq0fDwVDNlkEcM5d4JybambzmNlmRccjIiIiQ4uZjQOuBq4ys0VrfV1IKK8CfmBmowcoPBEZXFcAWdFB1NOQThbLHAFcZ2ZbFh2IiIiIDA0hybsKWB/YxTn3Ri83cRj+2caZdQ9ORAaVma0OrAfcUnQs9TRcksWDgH8BlythFBERkf4ys1Z8X4rfAH7knPtLb7cR+oh+tN6xiUghfgpMw1cxHzKGRbLonPsY2AT4N3CFmW1VbEQiIiLS5L4Vhp86587p60bMbH4zu7D0zKOINB8zWxjYHrhwqDRsUzKy6AAGi3PuAzPbGLgJ+J2Z3ahqHyIiItJHVwAbhBbYa7VTlXkfAxsAS+GvUUSk+fwIGAX8ruhA6m1I9rPYHTObB5jfOfeimbUA7W64fQgiIiLSa6EBm/OBXzrn/lPH7f4UOBn4qnPu7nptV0QGR8gp1nHO3Vt0LPU27JLFktAh7hnAWGB359yMgkMSERGRBmVm6wKXAxOA7zjnbu7tNqIk2xYgT+NLK7Y9FngBeBFYTzexRZqHmY0eyrUVh8Uzi914Hd8X4/1mtkLRwYiIiEhjMW8P4E5gOvDlviSKwR5h+BTn3HTg18CX8c89iUgTMLOVgZfNbIOiYxkowzZZdN7hwJbAksC/zGzXUOIoIiIiAv6m8unAbcBazrnHBmg/5wIHA7cO0PZFpI5C1dMzgVbgiYLDGTDDNlkscc5dD6wK/BM4CVio2IhERESkSGY2wsw+Eyb/gm+8Ykvn3AcDtU/nXLtz7rfOuXfMbLRuXos0vF/g+1X8mXPuvaKDGSjDPlkEcM69BmyEf07grVDl5CdmNm/RsYmIiMjgMbP1gX8A95jZWOfcTOfc2c65tkHa//xh/52qq4pIYwjVTo8GrgIuKjicAaVkMXDOtZVVLVkX3/hNbmaHKmkUEREZusJN4g3M7HrgbmAxfJXQIhqt+AB4FTjJzDYrYP8i0rMYeB7YZag3SKVksYrQ7O2q+OcTDgFeM7M/KWkUEREZkr4C3AV8CTgIWN45d75zrr3O+/luGLoU9rkj8B/gKjPbos4xiEgfmVlr+DPBN3b1UZHxDIZh23VGrczsC8D/AV8FVnbOzTGzbwAvA08P9bsJIiIiQ4mZjQM2BL4DvOacOyg8H/h94Ern3LRCAwzMbD58YzerAds4564sNiKR4c3MtgaOBTZ0zuUFhzNolCzWyMxanHNt4YTyEr4F1Rx/IL8DuNc590qBIYqIiEgXzOyH+ATxa/g+lj8G/uCc22+wYoiSbDJAnsbn1rK+mY0HTgYOcs69YWZzO+c+HrgIRaSSmX0OOAJfK+Ah4NvOuVeLjWrwjCw6gGZRerDdOefM7MvAVsDGwLbAj4E/AHuEZnQPA54Dng3DOyqBFBERGTihetiSwIrASmG8BLBJOAd/Bfgs8CfgOuAu59ysQQ5zchifW8vKzrmpwA/LZt1gZiOAs4DrnHPv1zU6EfmfUEB0AbADvo/Vg4FjnHOzCw1skClZ7IPQeuppwGlmNhL/fOPUsDgC9ufTn+3HZra3c+7PZrYYsC/wJvAO8BEwBXjMOfd2ONmNBqYqwRQRkeEk3HAdHYZRYfymc26WmS2D77R+3jAsik8GdwnN1h8E/KZsc28CTwIT8Y3G/GiwWjQdCCFJvAz4OT7ZbDOzR4DTw/VFC/4a5JUCkmCRphSqpc+Hv9H0uTAs5JzbJRQQfQwcBxzvnHunwFALo2Sxn5xzc4CHy6afD1+8pYDlwvBZfAkj+C/jbsD4ik1tA1wOTAJuAZyZTQdmh+F7zrm/heclTwRmlS2bDezpnHvCzL4G7AW0A65svL9z7hUz2xj/XEZpWWn5Ac6590LLa1tWeau/cs5NNbOtgG9UWf7TUE13W2CDimVznHN7A5jZzsDaFcs/cc4lYfmP8cl3ufecc4eE5f8HrFCx/HXn3NFh+T74k2W5F5xzvw/LDwQWqVj+X+fcGWH5ofiLkHKPOuf+HJYfDYyrWP6Ac+7isPwEOjccdY9z7opwI+A4OrvVOZeZ2Vz4ag6VMufcbaE59V9XWX6lc+7vZTciSko3Gy5xzj1kZksDe1ZZfoFz7j9mtgKwS5Xl5zjnnjWzzwPbV1l+ZvhurQF8u8ry00KXNF8CNquy/CTn3IehufpJFctnAac656aF7a8U5k3H32T5EHi80S8Aw0Veq3NuppmNwv8G5sIfB0rjB5xzD5vZROAn+O9RSxhG4L8HD5jZoviLxUqXhddHfPr/XFL6P3+OT5dUlPzROfeMma0K7FRl+SnOuZfMbG18jYpKxznn3gz/x29XWX6Ec+6DcAzavMryg8IxZgv882SV9g3HmO/iS4jKzXHO7QtgZjsCa1Usn+qc+3VY/kPgCxXL33POHR6W70X1Y0walu+DP76Xe7HiGLNoxfL/OudOD8sPp/ox5uyw/Fg6H2P+4Zy7MCw/Gf+dKHenc+6v4RhzIp3d7Jy71szmBo6psvwa59zNZrYAcHiV5Zc65+4ysyXxjb4Z/js5Ivx9VjgGfQ44tGz5SHyy91vn3H1m9hXgVDqSwNL4u865u81sO+CSKvv/Ir7q14b4ErWS94HX8Mnge8C1+MdEnsJ/5p/qE7HRjxM9CQ3fnGJmpwFrAt/Ct94+KqyyBL5WE2b2Ef4m9lTgEOfcJeHY8DtgThjawnCWc+5+M1sO329cpT845x4L54Bq3XmcFI4da/Lpc0jJceHYsS6wXZXlR4ZzxNfwtbYqHRLOEZsCm1ZZfoBzbrqZfZPO5xCHv35xZvYdfANGrmz5TOfcoQBmtg3+2FC+/GPn3PFh+bbA8vjPbEoY3nHO3Vglpj4Jv+Gl8ceQD51z/w7zD6DjN1P6/d8bftetwFFVNneHc+7GcG1xWJXlNzjnbg/XFgdVWX5F+F0vDvyqyvKLnHMPhps4P6+y/Gzn3L/NbCWqf29Oc849ZWarU/2c9Dvn3Ivhe/P9KsuPdM69bmZfp6PRKMMfd1rw//f3wnOG2+PPsxOAecKwYii5P7Ii/lnA4+a7zZnunBv2XdgoWRwAoXj6uTDcWLHsAWCu8ONdEJgb/6V9OqzyPLBfmD8Wf2Boxd8hBf+MxRNl80tD6eA2EV/1pnSyLo3HhOVL4A+m5ctG0HGB8Dmqt9T2a/xJZ5Uulu+NP4CuAXyvYtnMsBz8gbryQvM9fKtS4C8C44rlr+AvUAC+jm9sqNyT+L5uADbBn0TL/RP4ffh7SzpfCN6B7yoFYGv8Z1RuAvDn8Pd2+M+43Ejg4vD3znT+Xc0ErsAfvCbT2XtAhv8f7Vpl+cv4lnnnxncMXekp4O/4O2Ol5eWdOT+Mv9BahI4konz5vfhW95ai44BZvvx2/M2Oz+G/m5XLr8f/j1YFDqyy/FLgLfz//hA6+zM+6duA6heqZwHT8J99tRPWKPwd9t8C38RfLD4GPBKGFwazlN7MRuP/j6vjP7MlgMXxD8UfjP+931PlpQfg/1fz0vF9LnH4z/ABYAHgZ1Ve/5/w+kXxjXJVKv2fl6R6MnkT8Az+5tZPqiy/DP/ZroC/4VXpT/jj1Oep/j39Pb50ZzWqf88Pxx9jvtjF8v3wx5h16Pw7mknHjZKv0PmC9D06brRMAipbl3yJju/eRlQ/xqTh703onIyWH2O2oPox5vTw97fofIyZCzg7/P0dOh9jHHBh+HsbOh9jpgB/xR9jKo+/AK/jE6nRVD9+PwXcjL+Yqrb8IXxLoXPjb/iU32hsB64J643Hf+9Ly+bg/zejw/Jp+M96Jv6CrDQu3a1/DP8bmVWxvPRs0BX4bi0+wF9If6r0zDn3MGU3b4eqkDQ+GIZyH+F/O5/Bnw9KN6PeDcvnwn83R9JxQd2C/26Avyap9v+/Fv+/WZTq369L8MeOpaieDJ6N/78vi2/ltdKp+OPbSvhzaKVj8OeI1ah+Dv0N/gbi2nz6HFg6D5XOG1+vsnwq/gYH+N/mDmXLCXEdH/7+Pp1vpj9NuM4LN3reAP7snPuwSpxVhaqOO+AT7XXx137gqz+WPo/D8Nd6s/HHQfD/w2vx/8Nqx/SpIbYxVD9mv4Y/v89N9WPuk/hri3mp/rk/gP8OLkj1/+stwL/x35sdqiy/An/s+QzVvzfnAi/iCwCqfe9OwR/bluXT39vSjZDS57gg/rv1Cf438kYYl27s/xX/Xl8P8bwUCoIkUAM3IjLowsnxf8Jd39INjJIW/MlxWlg+HzA/Pjkci0/i53bOXR22+SP8hfpn8TdMWvAlD4s452ab2WeAV12dm8IPcX0zvI3zwvv4CH9Sfxyf7L+KL0G+PVRd/xr+xDW1bDwl3B0fgb+4bsNfdLepSrrI0BAl2Z0AeRpPKjYSqYWZWen4G6r5gk/SSjf6RzrnngnLb8LfTPoI+Ilz7i+92M+D+JtENwD/wp8znnehxc1QI2W2zgVSBCWLIjLkmNkYfAnXhJCgGb6kfxS+hOhPzrl+dbZtZsvj72hvi794uMs5NyksWxh4Wyd2ESkXJdk4gDyNG6J7Dqmv8LjEafgaEMcD+3V1HgjVau93zn1kZovgzxn17tdTpN+ULIrIkBfuCH8PX1XnK/hqs0fiqwv1uiEIM/sF/kJgBr6a7MXAQ0oORUSGt1B75GR8tdVVnHMvV1lnU3yLvGc55/Ya5BBFekXJoogMG6GEcUN8Q0LrANs65y7rxWtHO+dmmNk6+GfHjnXOvTVgAYvIkBIl2Z4AeRqf3tO60rzC4wSRc+6FKsuWxLc98TzwVefclMGOT6Q3KlttFBEZspx3G74Rga/gH2zHzJavfI6yXKhWegNwZtjOP5xz+yhRFJFe+h7VG+uQIcQ51+6ce8HMRpjZTmY2Fv530/F0/DP131GiKM1AyaKIDDshabw3NJzzGXyDAleGrgU+xcw2xLciOgl4oLukUkREpMyawPl09P+5Nb4htoOdcy8WFpVILyhZFJHh7lX8iXxL4O+hihDwvxZWbwLeBtZyzp2u5xJFRKQWzrkH8cniL8K55RF8VyAnFxqYSC8oWRSRYS1UFzoB31F8hC89XDN0UH4cvh+qdZ1zTxQYpoiINKeD8d1CHeKce945l6gfP2kmShZFRADn3C3AevhOwCc7594N01vouRIREemL0Brq6cAPzezLRccj0ltqDVVEREREREQ6UcmiiIiIiIiIdKJkUURERERERDpRsigiIiIiIiKdKFkUERERERGRTpQsioiIiIiISCdKFkVERERERKQTJYsiIiIiIiLSiZJFERERERER6UTJooiIiIiIiHSiZFGkQZnZuWbmqgzTzewlMzvbzBYe4BjuNLN8IPdRq8GIxcwODZ/xsd2s48zs3LLpc83M9XI/Nb/GzEaZ2eK92X543d0h1n26WD45LJ/Uw3ZqWq9erxOR5qJz1acNZixmtkz4rGeb2SL9iaevcTfSZy8DY2TRAYhIj34BvFs2PQ+wEbArsJaZfdE5N2uA9n0kMH6Att3IfmFm5zvnHq9h3TOB2wYiCDNbCrgFOBo4txevWxL4CjAV2AX43UDEJyJSRueqwbcD/jg/HtgROL7YcGQoUrIo0viuds7lFfNON7PTgT2ArYDLBmLHzrlbB2K7TWAk8AczW985120JoHPufuD+AYpjaWD5PrxuhzA+FdjfzNZyzj1Uv7BERDrRuWrw7QD8DYiAyShZlAGgaqgizeu8MF6n0CiGpuuA9fB3xJvRDsB/6fiOTC4uFBEZ5nSuGgBmtjqwInA3cAOwspmtVWxUMhQpWRRpXlPD2MpnmtkWZnafmU0zsw/M7Aoz61Q6ZWY7mtlj4bmSJ81sGzO7zczuLFun07MIZraKmV1tZh+G1/7DzLaqWOdOM7vJzDY1s4fMbIaZvRyeCezxuGNmG4X3MNXMnjezbbtYbyUzuyrEMs3M7jWzTbqI5bdm9omZvW1mq/QQwkHAG8AxZrZAD7F2ev7QzBYLz+m8Efb5YOVnFNZbK8Q33czeNLPfm9mYsGwy/o4xwJ978YzjysAXgDudc/8Fnga2N7PRXbxksfAZTjOzt8zsFDObp4d9jAmf54tmNsvMXjCzw81sVJXVFzazC8P/aErY12fKtlV6tnFVM7s4fGc/DutFVdabVBHLp+bXur2w7jxmdlr4P001s2vNbL3w+sndfQYiUjOdqwbmXPX9ML4TuCr8vUs3sW5pZk+E9/iYmX2/q3V7E3fZut+o+AwPKv8Ma/2sq/0vq83vzf/OzL5kZneEc8FrYZ3fWC/bGxiulCyKNK9Nw/iR0oxwgXst/uS8H3AC8GXggfKTsJntCVwAvA/8CrgLuARYs7sdmtkXgX8AX8I/B3cgMAq4ysz2qlh9FXyVozuBnwEvAIcAP+lhHxsBNwIT8EnbpcDZwBoV662Cr/65EnAU8GugFbihygn7K8D24b2eCzzZXQzAFPzzN/MDx/WwbmX88wEPhP1dAOwLTAeuNLNvVax+R4jl58A/wzgNy+4O7wvgLGCnGkMoXQBcHcZXAfMB3+xi/bOABYD9gWuAvYBrzMyqrWxmLcD1wD7479rPwvv4NXBFldedg/8c98d/9luG11W6FpgX/506M6zXnypr3W4vvI+bgN2BvwIJ/nOoFpuI9J3OVXU+V4VkaFvgNeAh/Dnndbq+MbgIcDn+BuSvgBnAhd3dFOtl3IsAV+DPBT8HXgKOwH+e5fr0WXejx+2Z2Zp0VNU9HPgjsHcYpBbOOQ0aNDTggD9ROGB1/EVsafgssCfwCf5E0hrWnwf4CLikYjuL4E+0V4XpuYAP8SfdlrL19g77u7Ns3p1AXjb9D+BjYImyeWOAh4FpwAJlr3PAlhXrvQ/c28P7fgh4GZinbN7XwvbyitieA8aXzRuJT7LeBEZVxDKphs/80LBuFKZvBtqB9cvWccC5lf+nsuljwjrrVbz354B/Vvxvf1G2zgjgWeDlsnmTwnqTa/zOGPBi+JxHhnlrhW1kFetODvPvLa0b5h9S/r8rW29SxfQmFdvbLcz/VsV6V1esd06Yv0zFeldUrHdGmL9ctTiqvI/K+Hra3k5h+kdl67TiL7pq/sw1aBjuAzpXFXGuKu3nlLJ5p4Z521SsW9runmXzRuMfVXiTjnNF5WfY27i/Xbbe3OF/fHeVOLr9rCvj6OZ/XOv2bgc+ABYsm7c60EbZuVtD14NKFkUa37+Ad8qG5/ClXdfhk5jZYb2N8Sfhq81sgdIAzMHf7dvEzEYCX8ffCT3JOddWtp8z8CVqVZlv+vxLwAXOuVdL851zM0I8Y0MMJdOArGK9p/EXBF3tYyH8HeNLnHNTyl77N+CxsvXmB76Kf05jbNl7nYgvSVsY+GLZpqfjT3C9tRcwEzjDzFprfM0WwMPOuXvL4p8BbA58t2LdS8rWacf/r7v8fGqwHv7u6XXOuTlhu6ULmk3MbNEqr/l9ad3g5DCOu9jH1vjv4cMV37Mb8CffLSrW/0vF9INhXPk+K0sRH+1ivVr1tL1v4y8g/lxaIfyWTujj/kSGO52rBu9cVapBcmXZvNLfk6us/yG+FkkpzplhemH8DcXK99fbuKdRVivDOfcx8BSdP8Nef9Y96HZ7ZjYv/qbrBc65d8rWewTf0rjUQK2hijS+HYG38KUem+ETmMuAPcKBseSzYVx5cV5uQWC58Pez5Qucc7PM7IVuXhuF8dNVlv03jJcqm/deSIDKzQRautlH6fXPV1n2FP4CADre60/DUM1n8KVmXcXSI+fcc2Z2NHAYvtpl2sNLwH9OnaoyOueeqbLu2xXT0/H/5y5Z57602spOgqVWUP9hn34+705gZ3xpWmUfkk9VxPmBmX1Ax/+70mfx36N3ulj+mYrpau8RfJWwcpXbmxnG3X1futPT9pYDXqy4CIWKz0NEaqZzlTeg5yrzz4ZvjS85fbnsWP9SmLeJmS3qnHuj7GXPV9wULI89wpfElutL3JXH0un4pLJcXz7r7vS0vWXoqLVT6Sk6qkhLN5QsijS+e11Hc+Q3mtmz+NKf+cxsKxfqVNBxcNwNXxWxmg/oSEZmVlk+o8q8kqrPsAWlWgrlfWj1OjnDVykBX5Wkq31Ax3s9jY5n8yo9UfZ35UmsN47B38U92Mwu6WllfGw1vfe+JLD4hnfKvQRE4U78NmHe6V28djKdk0VXZb0RdP2ZteBPvHt2sfyDiula32NfPotSPH3ZXiv+wqpSd78BEemazlWf3gcMzLkqxpfwgS+9rabyxmBXx/mu9tnbuAf6OA/Vj/W1HOeh998hKaNkUaTJOOdOMbMNgW/hHyT/fViUh/E7zrlPdRJvvqXIFvwBs3RHdnngmbJ1DH83savGX0rb/1yVZSuE8Ss1vYmu5fiTWrW+BZepEsucKu91JXz/hNP6GQvgq+uERhZuA06p4SUvA8tWzjSzH+AbL6hsXKG3Nq6YLpXUbYJ/TigD/lTldUcDK5rZ2s65f5bNjyg76ZvZgviqX9XumIP/7NcC7ihPdkM13e/Q/+9AV0oXNJWNN/S1+tILwBfNzMouYqGjNENE+kHnqk/FUs9zVakGyT50fEYli+JvFk7m08niZ7o51lU71g9E3LVqo/NxHvp2rC//DlXSsb5GemZRpDntjr/z+lszWzrMuxV/p+xX5c/Xmdni+FYu03CiuBl/kP9JRfPS38NX/anKOfcm/oH+Hc1sibLtjwJ+iT+596tjZOfcu/jnNXYMz52U9vFlylqYC9VrHgImm9liZeu14htQuZw63gxzzt2Of75wyxpWvwGfhPyvtb4Q16+AtZxzs7p8ZWelBOl//yfn3G0VQ6kaUOkZlmOdc1dXDnSUNlY2rf6jiul9w/jqLmK6Ft+66h4V83+Cr1a2UU9vqo/eDOPVSjNCaerWfdzeVfjk+ntl2xtB31vlE5HOdK6q47nKfLdGW+CToN9XOdafgW/EZ0Uz+1LZSxfCJ+2l7YzDH8NfouN57vL3N6jn2ApvAgtV7HdNqtyE7Ylz7m3gPnwrsfOWbW9pfFVpqYFKFkWakHPuLTPbH/+A+pnAN5xz75rZgfgGOu43swvxVTD2wleV2Te89iMz+w1wPHCbmV2Bv8P2E3zVnGrVVUpK3SQ8aGan46vx7Yh/0P9nzrkP6/D29gHuwT93dxowHt+NxbtdxPJwiOU9fJPjXwIOcM69V4dYyv0S30jNhB7WOxpfHfQOMzuF0Jw5vvPkqv1TdaP03N2O4W76eVWeO8HMxuO7xnjWOddV4wjn45+53M7Mfl42f30zuxqf5K6Hf7bxMufcHV1s50/AD4BTzGwNfJcfq+AvCv9FWYMxdXYn/iLiN2Y2Fv9s1M7470dfnIv/zl8QLvCexSeepY7Du/sdiEgNdK76VCz1OFd9B/8ZnVNRSljuTPznPRnfujP4hP18Mzsx7H9X/DOHW3XzOMRgn2NLLsGXnt5oZmfgn3v8Kf4YXa0v357siz9/PGhmf8CXWv6M7qsrSxmVLIo0rz8Bfwc2NrOdAZxzv8ffdZ2D7xcpwVff+bpz7q7SC51zv8OfmJfAn7A3xvfZ9DbV6/aXXnc/PqF4GH8A/i3+DvFWzrlaqmj2yDn3ML4VthfwXVn8KIxv7iKWh/An7ePwJ+vJzrlaGqLpbVxv4vuZ6mm9t/AJx3X4i5pj8CeljSur89SwrafwVV/XAk7k040ylNsK/967TNSccx/hT8ITw/ol2+FbBzwJ2BD/P92xm+3MDOv9LoxPxt/pPgN/ITggVZNCS4qb4vv92g/f6NADwI/7sb1NgIvoeL7nIzpKTLv8HYhIr+hcVb9z1ffxz+md1806F+Nbi93OzErPVD6Jf0Z0e/w5aRYQO+eu72ojg32OLdvv9fj/eem89F38cblPrZeG97Ep/ubrb/HP25+Mbz1Wx/kaWNc3JkRkKDLfYe/YandWzWwKvl+8nQc9MJFBZGbzAR+7jub8S/O3xlex2rCb0lURGWA6V0k9mNki4WZv5fzrgFWdc5UteEsFlSyKDD+LAR+YWVI+08xifEe6/6z6KpGhZW9gWvkzTcF2+NKORwY/JBEpo3OV1MMDZnZT+YzwnOnX0HeoJipZFBmGzOzv+IfwT8P3NfRZfNWMt4DVB6oqoUijMLOV8c9YPg/8Ed+QxjfwzwT91jl3cIHhiQg6V0n/mdlv8Y+QXAL8Df8oxm7A4sCXnHP/KS665qBkUWQYCq2CHQR8G3/39h3geuCgAXxoXaShhNYCD8E/Ezoe/8zU6c65PxYamIgAOldJ/4WWdPfCP9/+WXx3U/cCv3HO/bvI2JqFkkURERERERHpRM8sioiIiIiISCdKFkVERERERKQTJYsiIiIiIiLSiZJFERERERER6UTJooiIiIiIiHSiZFFEREREREQ6+X/RePm0pNscawAAAABJRU5ErkJggg==",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import norm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"fig, ax = plt.subplots(figsize=(16, 8))\n",
"x_min = -4\n",
"x_max = 4\n",
"x = np.linspace(x_min, x_max, 1000)\n",
"\n",
"mu = 0\n",
"sigma = 1\n",
"ax.plot(x, norm.pdf(x), color=\"C0\", linewidth=2)\n",
"\n",
"\n",
"ticks = [1.5]\n",
"for _x in ticks:\n",
" ax.axvline(_x, linestyle=\"dashed\")\n",
"\n",
"ax.axhline(0)\n",
"ax.axis(\"off\")\n",
"\n",
"ax.fill_between(x, norm.pdf(x), where=x >= ticks[0], color=\"r\", alpha=0.5)\n",
"\n",
"x, y = range_brace(\n",
" x_min,\n",
" ticks[0],\n",
" height=0.05,\n",
")\n",
"ax.plot(x, -y, \"--\", color=\"k\")\n",
"\n",
"\n",
"x, y = range_brace(\n",
" ticks[0],\n",
" x_max,\n",
" height=0.05,\n",
")\n",
"ax.plot(x, -y, \"--\", color=\"k\")\n",
"\n",
"ax.text(s=\"Ablehnen der $H_0$\", x=2, y=0.45, size=26)\n",
"ax.text(s=\"Nicht ablehnen der $H_0$\", x=-1.2, y=0.45, size=26)\n",
"\n",
"\n",
"ax.text(s=\"Region der Ablehnung\", x=2, y=-0.08, size=18)\n",
"ax.text(s=\"Region der Nicht-Ablehnung\", x=-2.2, y=-0.08, size=18)\n",
"\n",
"ax.text(s=r\"$1-\\alpha$\", x=-0.3, y=0.25, size=22)\n",
"\n",
"ax.annotate(\n",
" r\"$\\alpha$\",\n",
" xy=(2, 0.02),\n",
" xytext=(2.4, 0.1),\n",
" # textcoords=\"data\",\n",
" arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n",
" size=19,\n",
")\n",
"\n",
"ax.annotate(\n",
" r\"Kritischer Wert\",\n",
" xy=(ticks[0], 0.3),\n",
" xytext=(2.2, 0.3),\n",
" # textcoords=\"data\",\n",
" arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n",
" size=19,\n",
" verticalalignment=\"center\",\n",
")\n",
"\n",
"ax.set_ylim(-0.05, 0.5)"
]
},
{
"cell_type": "markdown",
"id": "bd416aad-a50c-4a17-afdb-252a6cf200b9",
"metadata": {},
"source": [
"### Der $p$-Wert-Ansatz"
]
},
{
"cell_type": "markdown",
"id": "775fff8c-fa93-4036-b7bd-a980ec22094e",
"metadata": {},
"source": [
"Bei der $p$-Wert-Methode wird die Wahrscheinlichkeit ($p$-Wert) des numerischen Wertes der Teststatistik mit dem angegebenen Signifikanzniveau ($\\alpha$) des Hypothesentests verglichen.\n",
"\n",
"Der $p$-Wert entspricht der Wahrscheinlichkeit, Stichprobendaten zu beobachten, die mindestens so extrem sind wie die tatsächlich erhaltene Teststatistik. Kleine $p$-Werte sind ein Beweis gegen die Nullhypothese. Je kleiner (näher an $0$) der $p$-Wert ist, desto stärker ist der Beweis gegen die Nullhypothese.\n",
"\n",
"Ist der $p$-Wert kleiner als oder gleich dem angegebenen Signifikanzniveau $\\alpha$ ist, wird die Nullhypothese abgelehnt; andernfalls wird die Nullhypothese nicht abgelehnt. Mit anderen Worten: wenn $p \\le \\alpha$, wird $H_0$ abgelehnt; andernfalls, wenn $p \\gt \\alpha$, wird $H_0$ nicht abgelehnt.\n",
"\n",
"Folglich kann durch die Kenntnis des $p$-Wertes jedes gewünschte Signifikanzniveau bewertet werden. Beträgt der $p$-Wert eines Hypothesentests beispielsweise $0,01$, kann die Nullhypothese auf jedem Signifikanzniveau größer oder gleich $0,01$ abgelehnt werden. Bei einem Signifikanzniveau kleiner als $0,01$ wird sie nicht verworfen. Daher wird der $p$-Wert in der Regel verwendet, um die Stärke des Beweises gegen die Nullhypothese ohne Bezug auf das Signifikanzniveau zu bewerten.\n",
"\n",
"Die folgende Tabelle enthält Leitlinien für die Verwendung des $p$-Werts zur Bewertung der Beweise gegen die Nullhypothese (*{cite:t}`fahrmeirstatistik` s.388*)."
]
},
{
"cell_type": "markdown",
"id": "c16f85cf-c418-4411-9fd0-1de813a6469a",
"metadata": {},
"source": [
"$$\n",
"\\begin{array}{l|l}\n",
"\\hline\n",
" \\text{$p$-Wert} & \\text{Hinweise gegen } H_0 \\\\\n",
"\\hline\n",
"\\ p > 0,10 & \\text{Schwache oder keine Hinweise } \\\\\n",
"\\ 0,05 < p \\le 0,10 & \\text{Mäßiger Hinweis } \\\\\n",
"\\ 0,01 < p \\le 0,05 & \\text{Starker Hinweis} \\\\\n",
"\\ p \\le 0,01 & \\text{Sehr starker Hinweis} \\\\\n",
"\\hline \n",
"\\end{array}\n",
"$$"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
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