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[lab-inferential-statistics] Karolin Diede #11

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173 changes: 173 additions & 0 deletions .ipynb_checkpoints/Solutions-checkpoint.ipynb
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Lab | Inferential statistics"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- It is assumed that the mean systolic blood pressure is `μ = 120 mm Hg`. In the Honolulu Heart Study, a sample of `n = 100` people had an average systolic blood pressure of 130.1 mm Hg with a standard deviation of 21.21 mm Hg. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1. Is the group significantly different (with respect to systolic blood pressure!) from the regular population?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1.1 Set up the hypothesis test."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"H0 = 120\n",
"HA =! 120"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1.2 Write down all the steps followed for setting up the test."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"import math\n",
"\n",
"sample_mean = 130.1\n",
"pop_mean = 120\n",
"sample_std = 21.21\n",
"n = 100"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"from scipy.stats import ttest_ind, norm\n",
"sample = norm.rvs(loc=sample_mean, scale=sample_std, size=n)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([125.87272186, 147.33041173, 148.31785028, 112.04380437,\n",
" 109.29670776, 142.88049757, 89.87184986, 144.59255735,\n",
" 143.98751965, 164.13942162, 150.14885634, 148.8038505 ,\n",
" 128.61028065, 97.73265084, 138.41288628, 148.81005023,\n",
" 89.80889773, 155.34525738, 94.20433297, 118.01147848,\n",
" 140.33613584, 98.86538375, 120.84419938, 125.50754501,\n",
" 169.98167304, 141.64637665, 122.23356583, 118.33330743,\n",
" 136.95867209, 138.49118087, 156.95988839, 98.2508438 ,\n",
" 105.38052451, 136.69245243, 127.63471356, 121.13244895,\n",
" 123.20426934, 130.25377353, 139.0563798 , 92.73221543,\n",
" 116.59123023, 131.78706465, 160.76714288, 150.08038636,\n",
" 138.16101622, 147.63416238, 115.39205312, 154.02299445,\n",
" 71.19098511, 167.47047571, 131.10517644, 113.06360969,\n",
" 143.55792341, 132.26443597, 82.90132016, 120.84780507,\n",
" 134.02454364, 98.29619475, 126.99829157, 144.19791731,\n",
" 145.6729652 , 148.25716342, 123.13796532, 99.30986144,\n",
" 156.64771966, 137.99025548, 116.97487254, 130.85454744,\n",
" 138.81399206, 127.17536482, 140.91634457, 109.51305907,\n",
" 145.28927328, 152.36994104, 115.37969632, 121.37670788,\n",
" 152.46644509, 136.32657518, 153.70028065, 116.50992758,\n",
" 139.82744355, 145.91862428, 101.27965477, 134.87463457,\n",
" 114.09559859, 152.65867141, 128.41457124, 128.41892265,\n",
" 136.86075007, 153.13865868, 141.7593169 , 110.19926965,\n",
" 120.78665058, 106.86669336, 114.7615379 , 125.5866693 ,\n",
" 132.16603016, 103.11045235, 80.66212071, 125.76824276])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sample"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1.3 Calculate the test statistic by hand and also code it in Python. It should be 4.76190. We will take a look at how to make decisions based on this calculated value."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4.761904761904759"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"statistic = (sample_mean - pop_mean)/(sample_std/math.sqrt(n))\n",
"statistic"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2. If you finished the previous question, please go through the code for principal_component_analysis_example provided in the files_for_lab folder ."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.8.5"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
100 changes: 84 additions & 16 deletions Solutions.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -2,31 +2,27 @@
"cells": [
{
"cell_type": "markdown",
"id": "e00a11f1",
"metadata": {},
"source": [
"# Lab | Inferential statistics"
]
},
{
"cell_type": "markdown",
"id": "2c813f0a",
"metadata": {},
"source": [
"- It is assumed that the mean systolic blood pressure is `μ = 120 mm Hg`. In the Honolulu Heart Study, a sample of `n = 100` people had an average systolic blood pressure of 130.1 mm Hg with a standard deviation of 21.21 mm Hg. "
]
},
{
"cell_type": "markdown",
"id": "120875d3",
"metadata": {},
"source": [
"## 1. Is the group significantly different (with respect to systolic blood pressure!) from the regular population?"
]
},
{
"cell_type": "markdown",
"id": "d26c43d4",
"metadata": {},
"source": [
"### 1.1 Set up the hypothesis test."
Expand All @@ -35,46 +31,118 @@
{
"cell_type": "code",
"execution_count": null,
"id": "39c6f717",
"metadata": {},
"outputs": [],
"source": []
"source": [
"H0 = 120\n",
"HA =! 120"
]
},
{
"cell_type": "markdown",
"id": "17c9988a",
"metadata": {},
"source": [
"### 1.2 Write down all the steps followed for setting up the test."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b09ce149",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": []
"source": [
"import math\n",
"\n",
"sample_mean = 130.1\n",
"pop_mean = 120\n",
"sample_std = 21.21\n",
"n = 100"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"from scipy.stats import ttest_ind, norm\n",
"sample = norm.rvs(loc=sample_mean, scale=sample_std, size=n)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([125.87272186, 147.33041173, 148.31785028, 112.04380437,\n",
" 109.29670776, 142.88049757, 89.87184986, 144.59255735,\n",
" 143.98751965, 164.13942162, 150.14885634, 148.8038505 ,\n",
" 128.61028065, 97.73265084, 138.41288628, 148.81005023,\n",
" 89.80889773, 155.34525738, 94.20433297, 118.01147848,\n",
" 140.33613584, 98.86538375, 120.84419938, 125.50754501,\n",
" 169.98167304, 141.64637665, 122.23356583, 118.33330743,\n",
" 136.95867209, 138.49118087, 156.95988839, 98.2508438 ,\n",
" 105.38052451, 136.69245243, 127.63471356, 121.13244895,\n",
" 123.20426934, 130.25377353, 139.0563798 , 92.73221543,\n",
" 116.59123023, 131.78706465, 160.76714288, 150.08038636,\n",
" 138.16101622, 147.63416238, 115.39205312, 154.02299445,\n",
" 71.19098511, 167.47047571, 131.10517644, 113.06360969,\n",
" 143.55792341, 132.26443597, 82.90132016, 120.84780507,\n",
" 134.02454364, 98.29619475, 126.99829157, 144.19791731,\n",
" 145.6729652 , 148.25716342, 123.13796532, 99.30986144,\n",
" 156.64771966, 137.99025548, 116.97487254, 130.85454744,\n",
" 138.81399206, 127.17536482, 140.91634457, 109.51305907,\n",
" 145.28927328, 152.36994104, 115.37969632, 121.37670788,\n",
" 152.46644509, 136.32657518, 153.70028065, 116.50992758,\n",
" 139.82744355, 145.91862428, 101.27965477, 134.87463457,\n",
" 114.09559859, 152.65867141, 128.41457124, 128.41892265,\n",
" 136.86075007, 153.13865868, 141.7593169 , 110.19926965,\n",
" 120.78665058, 106.86669336, 114.7615379 , 125.5866693 ,\n",
" 132.16603016, 103.11045235, 80.66212071, 125.76824276])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sample"
]
},
{
"cell_type": "markdown",
"id": "63df3700",
"metadata": {},
"source": [
"### 1.3 Calculate the test statistic by hand and also code it in Python. It should be 4.76190. We will take a look at how to make decisions based on this calculated value."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "97f73e20",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"data": {
"text/plain": [
"4.761904761904759"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"statistic = (sample_mean - pop_mean)/(sample_std/math.sqrt(n))\n",
"statistic"
]
},
{
"cell_type": "markdown",
"id": "4a7564e5",
"metadata": {},
"source": [
"## 2. If you finished the previous question, please go through the code for principal_component_analysis_example provided in the files_for_lab folder ."
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