![\"Skills](\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/assets/logos/SN_web_lightmode.png\")
\n",
" \n",
"\n",
" \n",
" \n",
" \n",
"
norm.cdf function\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.1847801491443654\n"
]
}
],
"source": [
"x1 = 3.5\n",
"prob1 = scipy.stats.norm.cdf((x1 - eval_mean)/eval_sd)\n",
"print(prob1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Then for less than 4.2\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.642057540461896\n"
]
}
],
"source": [
"x2 = 4.2\n",
"prob2 = scipy.stats.norm.cdf((x2 - eval_mean)/eval_sd)\n",
"print(prob2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The probability of a teacher receiving an evaluation score that is between 3.5 and 4.2 is:\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"45.7"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"round((prob2 - prob1)*100, 1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Using the two-tailed test from a normal distribution:\n",
"\n",
"* A professional basketball team wants to compare its performance with that of players in a regional league.\n",
"* The pros are known to have a historic mean of 12 points per game with a standard deviation of 5.5.\n",
"* A group of 36 regional players recorded on average 10.7 points per game.\n",
"* The pro coach would like to know whether his professional team scores on average are different from that of the regional players.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"State the null hypothesis\n",
"\n",
"* $H\\_0$: $x = µ\\_1$ (\"The mean point of the regional players is not different from the historic mean\")\n",
"* $H\\_1$: $x ≠ µ\\_1$ (\"The mean point of the regional players is different from the historic mean\")\n"
]
},
{
"attachments": {
"image.png": {
"image/png": "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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
"When the population standard deviation is given and we are asked to deal with a sub-sample, the size (n) of the sub-sample is used in the formula:\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.156"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"## because it is a two-tailed test we multiply by 2\n",
"2*round(scipy.stats.norm.cdf((10.7 - 12)/(5.5/sqrt(36))), 3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Conclusion:** Because the p-value is greater than 0.05, we fail to reject the null hypothesis as there is no sufficient evidence to prove that the mean point of the regional players is different from the historic mean\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Practice Questions\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Question 1: Using the teachers' rating dataset, what is the probability of receiving an evaluation score greater than 3.3?\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.8957422041794154\n"
]
}
],
"source": [
"## insert code here\n",
"prob = scipy.stats.norm.cdf((3.3 - eval_mean)/eval_sd)\n",
"print(1 - prob)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click **here** for the solution.\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Question 2: Using the teachers' rating dataset, what is the probability of receiving an evaluation score between 2 and 3?\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.6"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"## insert code here\n",
"prob_1 = scipy.stats.norm.cdf((2 - eval_mean)/eval_sd)\n",
"prob_2 = scipy.stats.norm.cdf((3 - eval_mean)/eval_sd)\n",
"round((prob_2 - prob_1)*100,1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click **here** for the solution.\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Question 3: To test the hypothesis that sleeping for at least 8 hours makes one smarter, 12 people who have slept for at least 8 hours every day for the past one year have their IQ tested.\n",
"\n",
"* Here are the results: 116, 111, 101, 120, 99, 94, 106, 115, 107, 101, 110, 92\n",
"* Test using the following hypotheses: H0: μ = 100 or Ha: μ > 100\n"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"IQ mean is 106.0, sd is 8.831760866327848, variance is 78.00000000000001\n"
]
}
],
"source": [
"## insert code here\n",
"IQs = [116, 111, 101, 120, 99, 94, 106, 115, 107, 101, 110, 92]\n",
"n = len(IQs)\n",
"mean = sum(IQs)/n\n",
"mean_diff = [(iq-mean) ** 2 for iq in IQs]\n",
"std = sqrt(sum(mean_diff)/(n-1))\n",
"variance = std ** 2\n",
"print(f\"IQ mean is {mean}, sd is {std}, variance is {variance}\")\n",
"t = scipy.stats.norm.cdf((mean-100)/(std/sqrt(n)))"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.009"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"round(1-t,3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click **here** for a hint.\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click **here** for the solution.\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Authors\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Aije Egwaikhide](https://www.linkedin.com/in/aije-egwaikhide/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkST0151ENSkillsNetwork20531532-2022-01-01) is a Data Scientist at IBM who holds a degree in Economics and Statistics from the University of Manitoba and a Post-grad in Business Analytics from St. Lawrence College, Kingston. She is a current employee of IBM where she started as a Junior Data Scientist at the Global Business Services (GBS) in 2018. Her main role was making meaning out of data for their Oil and Gas clients through basic statistics and advanced Machine Learning algorithms. The highlight of her time in GBS was creating a customized end-to-end Machine learning and Statistics solution on optimizing operations in the Oil and Gas wells. She moved to the Cognitive Systems Group as a Senior Data Scientist where she will be providing the team with actionable insights using Data Science techniques and further improve processes through building machine learning solutions. She recently joined the IBM Developer Skills Network group where she brings her real-world experience to the courses she creates.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Change Log\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"| Date (YYYY-MM-DD) | Version | Changed By | Change Description |\n",
"| ----------------- | ------- | --------------- | -------------------------------------- |\n",
"| 2020-08-14 | 0.1 | Aije Egwaikhide | Created the initial version of the lab |\n",
"| 2022-05-11 | 0.2 | Lakshmi Holla | Updated markdown solution |\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Copyright © 2020 IBM Corporation. This notebook and its source code are released under the terms of the [MIT License](https://cognitiveclass.ai/mit-license/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkST0151ENSkillsNetwork20531532-2022-01-01).\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python",
"language": "python",
"name": "conda-env-python-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.12"
}
},
"nbformat": 4,
"nbformat_minor": 4
}