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[lab_inferential_statistics] Elissa de Jong #5

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206 changes: 206 additions & 0 deletions .ipynb_checkpoints/Solutions-checkpoint.ipynb
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Original file line number Diff line number Diff line change
@@ -0,0 +1,206 @@
{
"cells": [
{
"cell_type": "markdown",
"id": "e00a11f1",
"metadata": {},
"source": [
"# Lab | Inferential statistics"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "20e95bfe",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import math\n",
"from scipy.stats import ttest_1samp"
]
},
{
"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."
]
},
{
"cell_type": "markdown",
"id": "07ffa509",
"metadata": {},
"source": [
"The null hypothesis is as follows:<br> \n",
"H0 : μ = 120<br>\n",
"The alternative hypothesis (two-tailed) is as follows:<br>\n",
"HA : μ != 120<br>"
]
},
{
"cell_type": "markdown",
"id": "17c9988a",
"metadata": {},
"source": [
"### 1.2 Write down all the steps followed for setting up the test."
]
},
{
"cell_type": "markdown",
"id": "9d420004",
"metadata": {},
"source": [
"- sample mean = 130.1\n",
"- mean population = 120\n",
"- standard deviation sample = 21.21\n",
"- sample size = 100\n",
"<br>\n",
"t = (130.1 - 120) / (21.21 / sqrt100) \n",
"<br>\n",
"- calculate/code the value of the test statistic \n",
"- find the T-critical from the T-table. Use the degrees of freedom (100 in this case) and the alpha level (0.05) to find the T-critical value. For a two-tailed t-test with a 100 dof the critical rejection region equals to t<=-1.984 and t=>1.984. \n",
"- check if the test statistic falls in the rejection region OR:\n",
"- calculate/code the p-value to check if the test statistic is significantly different from the population statistic so the null hypothesis should be rejected (p-value is less than 0.05 or 0.01) "
]
},
{
"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": 2,
"id": "97f73e20",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4.761904761904759"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"t = (130.1-120) / (21.21 / (math.sqrt(100)))\n",
"t"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "f25cbd29",
"metadata": {},
"outputs": [],
"source": [
"sample_mean = 130.1\n",
"sample_stdev = 21.21"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "0d01ae23",
"metadata": {},
"outputs": [],
"source": [
"x = np.random.normal(loc = sample_mean, scale = sample_stdev, size = 100)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "d23efac6",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"4.82524640921731 5.07938051235794e-06\n"
]
}
],
"source": [
"popmean = 120\n",
"t_statistic, p_value = ttest_1samp(x, popmean)\n",
"print(t_statistic, p_value)"
]
},
{
"cell_type": "markdown",
"id": "ed8f9213",
"metadata": {},
"source": [
"Its not giving the right/same test statistic. How do i code the distribution in the correct way so the sample mean and sample standard deviation are fixed? "
]
},
{
"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 ."
]
}
],
"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": "3.9.5"
},
"toc": {
"base_numbering": 1,
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": false,
"toc_position": {},
"toc_section_display": true,
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 5
}
129 changes: 115 additions & 14 deletions Solutions.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -8,6 +8,18 @@
"# Lab | Inferential statistics"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "20e95bfe",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import math\n",
"from scipy.stats import ttest_1samp"
]
},
{
"cell_type": "markdown",
"id": "2c813f0a",
Expand All @@ -33,12 +45,15 @@
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "39c6f717",
"cell_type": "markdown",
"id": "07ffa509",
"metadata": {},
"outputs": [],
"source": []
"source": [
"The null hypothesis is as follows:<br> \n",
"H0 : μ = 120<br>\n",
"The alternative hypothesis (two-tailed) is as follows:<br>\n",
"HA : μ != 120<br>"
]
},
{
"cell_type": "markdown",
Expand All @@ -49,12 +64,22 @@
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b09ce149",
"cell_type": "markdown",
"id": "9d420004",
"metadata": {},
"outputs": [],
"source": []
"source": [
"- sample mean = 130.1\n",
"- mean population = 120\n",
"- standard deviation sample = 21.21\n",
"- sample size = 100\n",
"<br>\n",
"t = (130.1 - 120) / (21.21 / sqrt100) \n",
"<br>\n",
"- calculate/code the value of the test statistic \n",
"- find the T-critical from the T-table. Use the degrees of freedom (100 in this case) and the alpha level (0.05) to find the T-critical value. For a two-tailed t-test with a 100 dof the critical rejection region equals to t<=-1.984 and t=>1.984. \n",
"- check if the test statistic falls in the rejection region OR:\n",
"- calculate/code the p-value to check if the test statistic is significantly different from the population statistic so the null hypothesis should be rejected (p-value is less than 0.05 or 0.01) "
]
},
{
"cell_type": "markdown",
Expand All @@ -66,11 +91,74 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 2,
"id": "97f73e20",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4.761904761904759"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"t = (130.1-120) / (21.21 / (math.sqrt(100)))\n",
"t"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "f25cbd29",
"metadata": {},
"outputs": [],
"source": []
"source": [
"sample_mean = 130.1\n",
"sample_stdev = 21.21"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "0d01ae23",
"metadata": {},
"outputs": [],
"source": [
"x = np.random.normal(loc = sample_mean, scale = sample_stdev, size = 100)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "d23efac6",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"4.82524640921731 5.07938051235794e-06\n"
]
}
],
"source": [
"popmean = 120\n",
"t_statistic, p_value = ttest_1samp(x, popmean)\n",
"print(t_statistic, p_value)"
]
},
{
"cell_type": "markdown",
"id": "ed8f9213",
"metadata": {},
"source": [
"Its not giving the right/same test statistic. How do i code the distribution in the correct way so the sample mean and sample standard deviation are fixed? "
]
},
{
"cell_type": "markdown",
Expand All @@ -83,7 +171,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
Expand All @@ -97,7 +185,20 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.5"
"version": "3.9.5"
},
"toc": {
"base_numbering": 1,
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": false,
"toc_position": {},
"toc_section_display": true,
"toc_window_display": false
}
},
"nbformat": 4,
Expand Down
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