Exercises - Week 1 to 6 of Statistics for Data Science with Python/1. Introduction_to_probability_distribution.ipynb

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   "source": [
    "<center>\n",
    "    <img src=\"https://gitlab.com/ibm/skills-network/courses/placeholder101/-/raw/master/labs/module%201/images/IDSNlogo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\"  />\n",
    "</center>\n"
   ]
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   "cell_type": "markdown",
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   "source": [
    "# **Introduction to Probability Distribution**\n"
   ]
  },
  {
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   "source": [
    "Estimated time needed: **30** minutes\n"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "In this lab, you will familiarize yourself with the normal probability distributions and work on some exercises\n"
   ]
  },
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   "metadata": {},
   "source": [
    "## Objectives\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-   Import Libraries\n",
    "-   Introduction to Probability Distributions\n",
    "    -   Normal Distributions\n",
    "-   Lab Exercises\n"
   ]
  },
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   "source": [
    "* * *\n"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import Libraries\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All Libraries required for this lab are listed below. The libraries pre-installed on Skills Network Labs are commented. If you run this notebook in a different environment, e.g. your desktop, you may need to uncomment and install certain libraries.\n"
   ]
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   "cell_type": "code",
   "execution_count": 1,
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   "source": [
    "# !pip install pandas\n",
    "# !pip install numpy\n",
    "# !pip install matplotlib\n",
    "# !pip install math\n",
    "# !pip install scipy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import the libraries we need for the lab\n"
   ]
  },
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   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats\n",
    "from math import sqrt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Read in the csv file from the url using the request library\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "ratings_url = 'teachingratings.csv'\n",
    "ratings_df = pd.read_csv(ratings_url)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction to Probability Distribution\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section, you will learn how to create the plot distributions using the scipy library in python\n"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normal Distribution\n"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "A normal distribution is a bell-shaped density curve described by its mean μ and standard deviation σ. The curve is symmetrical and centered around it's mean. A normal distribution curve looks like this:\n"
   ]
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize the curve. Import norm from scipy.stat and plot graph with matplotlib\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "# Plot between -4 and 4 with 0.1 steps.\n",
    "x_axis = np.arange(-4, 4, 0.1)\n",
    "# Mean = 0, SD = 1.\n",
    "plt.plot(x_axis, norm.pdf(x_axis, 0, 1))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lab Exercises\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using the teachers' rating dataset, what is the probability of receiving an evaluation score of greater than 4.5\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find the mean and standard deviation of teachers' evaluation scores\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.998 0.555\n"
     ]
    }
   ],
   "source": [
    "eval_mean = round(ratings_df['eval'].mean(), 3)\n",
    "eval_sd = round(ratings_df['eval'].std(), 3)\n",
    "print(eval_mean, eval_sd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the scipy.stats module. Because python only looks to the left i.e. less than, we do a remove the probability from 1 to get the other side of the tail\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1828639734596742\n"
     ]
    }
   ],
   "source": [
    "prob0 = scipy.stats.norm.cdf((4.5 - eval_mean)/eval_sd)\n",
    "print(1 - prob0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using the teachers' rating dataset, what is the probability of receiving an evaluation score greater than 3.5 and less than 4.2\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we find the probability of getting evaluation scores less than 3.5 using the <code>norm.cdf</code> function\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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": 8,
   "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": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "45.7"
      ]
     },
     "execution_count": 9,
     "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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U7VHEQBL/FbjmhmyMWpLGEBCxGsMv1adZYKbjs/E2CUEt7kYtDtmDaHym1TuaJlGmoqQhYuWoJZlXMSfCjCMJQVHBYeqOXPzFBETSOAIiVuMYppIC5hdM/jFqTFLcnA1SYbZSZIVCkritKy0Ra10INUm4UzZghp+k4Ml2s802s6MW7qklySAgYiWDo/dUUNdDAPbwJS3Mr/bZZ59g21PS6f8/pidi5aTVMeGIu+aVk6oVspgiViGbVZXKGgERK+sWUP6FREDEKmSzqlJZIyBiZd0Cyr+QCIhYhWxWVSprBESsrFtA+RcSARGrkM2qSmWNgIiVdQso/0IiIGIVsllVqawRELGybgHlX0gERKxCNqsqlTUCIlbWLaD8C4nAf7Sxhb28Il0QAAAAAElFTkSuQmCC"
    }
   },
   "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",
    "![image.png](attachment:image.png)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.156"
      ]
     },
     "execution_count": 10,
     "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": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8957422041794154\n"
     ]
    }
   ],
   "source": [
    "##calculate the probability less than 3.3\n",
    "prob_less_than = scipy.stats.norm.cdf((3.3 - eval_mean)/eval_sd)\n",
    "##then remove the probability from 1 to get the area to the right of 3.3\n",
    "print(1 - prob_less_than)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click **here** for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "##calculate the probability less than 3.3\n",
    "prob_less_than = scipy.stats.norm.cdf((3.3 - eval_mean)/eval_sd)\n",
    "##then remove the probability from 1 to get the area to the right of 3.3\n",
    "print(1 - prob_less_than)\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": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1847801491443654\n",
      "0.642057540461896\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "45.7"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## find the probablity of reciving a score of less than 2\n",
    "prob_less_than_2 = scipy.stats.norm.cdf((x1 - eval_mean)/eval_sd)\n",
    "print(prob_less_than_2)\n",
    "\n",
    "## find the probablity of reciving a score of less than 3\n",
    "prob_less_than_3 = scipy.stats.norm.cdf((x2 - eval_mean)/eval_sd)\n",
    "print(prob_less_than_3)\n",
    "\n",
    "## remove both probabilities from each other\n",
    "round((prob_less_than_3 - prob_less_than_2)*100, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click **here** for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "## find the probablity of reciving a score of less than 2\n",
    "prob_less_than_2 = scipy.stats.norm.cdf((x1 - eval_mean)/eval_sd)\n",
    "print(prob_less_than_2)\n",
    "\n",
    "## find the probablity of reciving a score of less than 3\n",
    "prob_less_than_3 = scipy.stats.norm.cdf((x2 - eval_mean)/eval_sd)\n",
    "print(prob_less_than_3)\n",
    "\n",
    "## remove both probabilities from each other\n",
    "round((prob_less_than_3 - prob_less_than_2)*100, 1)\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": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.007"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### find the mean and standard deviation of the 12 IQs\n",
    "iq_mean = np.mean([116, 111, 101, 120, 99, 94, 106, 115, 107, 101, 110, 92])\n",
    "iq_std = np.std([116, 111, 101, 120, 99, 94, 106, 115, 107, 101, 110, 92])\n",
    "\n",
    "### remember to remove from 1 because we want the value for when IQs are greater than 100\n",
    "round(1-scipy.stats.norm.cdf((iq_mean - 100)/(iq_std/sqrt(12))), 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click **here** for a hint.\n",
    "\n",
    "<!-- The hint is below:\n",
    "### find the mean and standard deviation of the 12 IQs\n",
    "iq_mean = np.mean([116, 111, 101, 120, 99, 94, 106, 115, 107, 101, 110, 92])\n",
    "iq_std = np.std([116, 111, 101, 120, 99, 94, 106, 115, 107, 101, 110, 92])\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click **here** for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "### remember to remove from 1 because we want the value for when IQs are greater than 100\n",
    "round(1-scipy.stats.norm.cdf((iq_mean - 100)/(iq_std/sqrt(12))), 3)\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Authors\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Aije Egwaikhide](https://www.linkedin.com/in/aije-egwaikhide?cm_mmc=Email_Newsletter-_-Developer_Ed%2BTech-_-WW_WW-_-SkillsNetwork-Courses-IBMDeveloperSkillsNetwork-ST0151EN-SkillsNetwork-20531532&cm_mmca1=000026UJ&cm_mmca2=10006555&cm_mmca3=M12345678&cvosrc=email.Newsletter.M12345678&cvo_campaign=000026UJ) 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"
   ]
  },
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   "source": [
    "## Change Log\n"
   ]
  },
  {
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   "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"
   ]
  },
  {
   "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?cm_mmc=Email_Newsletter-_-Developer_Ed%2BTech-_-WW_WW-_-SkillsNetwork-Courses-IBMDeveloperSkillsNetwork-ST0151EN-SkillsNetwork-20531532&cm_mmca1=000026UJ&cm_mmca2=10006555&cm_mmca3=M12345678&cvosrc=email.Newsletter.M12345678&cvo_campaign=000026UJ&cm_mmc=Email_Newsletter-_-Developer_Ed%2BTech-_-WW_WW-_-SkillsNetwork-Courses-IBMDeveloperSkillsNetwork-ST0151EN-SkillsNetwork-20531532&cm_mmca1=000026UJ&cm_mmca2=10006555&cm_mmca3=M12345678&cvosrc=email.Newsletter.M12345678&cvo_campaign=000026UJ&cm_mmc=Email_Newsletter-_-Developer_Ed%2BTech-_-WW_WW-_-SkillsNetwork-Courses-IBMDeveloperSkillsNetwork-ST0151EN-SkillsNetwork-20531532&cm_mmca1=000026UJ&cm_mmca2=10006555&cm_mmca3=M12345678&cvosrc=email.Newsletter.M12345678&cvo_campaign=000026UJ&cm_mmc=Email_Newsletter-_-Developer_Ed%2BTech-_-WW_WW-_-SkillsNetwork-Courses-IBMDeveloperSkillsNetwork-ST0151EN-SkillsNetwork-20531532&cm_mmca1=000026UJ&cm_mmca2=10006555&cm_mmca3=M12345678&cvosrc=email.Newsletter.M12345678&cvo_campaign=000026UJ).\n"
   ]
  }
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