hw05.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Homework 5: Hypothesis Testing\n",
    "\n",
    "This assignment is due Thursday, October 12 at 11:59PM. Before you begin, execute the following cell to load the provided tests. Each time you start your server, you will need to execute this cell again to load the tests.\n",
    "\n",
    "Reading: Chapter [10](https://www.inferentialthinking.com/chapters/10/testing-hypotheses.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the cell below to prepare the notebook and the tests. **Passing the automatic tests does not guarantee full credit on any question.** The tests are provided to help catch some common errors, but it is *your* responsibility to answer the questions correctly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=====================================================================\n",
      "Assignment: Homework 5: Hypothesis Testing\n",
      "OK, version v1.12.5\n",
      "=====================================================================\n",
      "\n",
      "\n",
      "Open the following URL:\n",
      "\n",
      "https://okpy.org/client/login/\n",
      "\n",
      "After logging in, copy the code from the web page and paste it into the box.\n",
      "Then press the \"Enter\" key on your keyboard.\n",
      "\n",
      "Paste your code here: A1yr8FY9FfHa32N5AWJMoTtrw1RUAO\n",
      "Successfully logged in as kcs1992@berkeley.edu\n"
     ]
    }
   ],
   "source": [
    "# Don't change this cell; just run it. \n",
    "\n",
    "import numpy as np\n",
    "from datascience import *\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plots\n",
    "plots.style.use('fivethirtyeight')\n",
    "\n",
    "from client.api.notebook import Notebook\n",
    "ok = Notebook('hw05.ok')\n",
    "_ = ok.auth(inline=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once you're finished, select \"Save and Checkpoint\" in the File menu and then execute the `submit` cell below. The result will contain a link that you can use to check that your assignment has been submitted successfully. If you submit more than once before the deadline, we will only grade your final submission."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "IPython.notebook.save_checkpoint();"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = ok.submit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Catching Cheaters\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose you are a casino owner, and your casino runs a very simple game of chance.  The dealer flips a coin.  The customer wins \\$9 from the casino if it comes up heads and loses \\$10 if it comes up tails."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"hide\">\\pagebreak</div>\n",
    "**Question 1.** Assuming no one is cheating and the coin is fair, if a customer plays twice, what is the chance they make money?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "manual_grade": true,
    "manual_problem_id": "catching_cheaters_1"
   },
   "outputs": [],
   "source": [
    "p_winning_after_two_flips = 1/4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Running tests\n",
      "\n",
      "---------------------------------------------------------------------\n",
      "Test summary\n",
      "    Passed: 1\n",
      "    Failed: 0\n",
      "[ooooooooook] 100.0% passed\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = ok.grade('q1_1')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A certain customer plays the game 20 times and wins 13 of the bets.  You suspect that the customer is cheating!  That is, you think that their chance of winning is higher than the normal chance of winning.\n",
    "\n",
    "You decide to test your hunch using the outcomes of the 20 games you observed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"hide\">\\pagebreak</div>\n",
    "#### Question 2\n",
    "Define the null hypothesis and alternative hypothesis for this investigation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "for_assignment_type": "student",
    "manual_grade": true,
    "manual_problem_id": "catching_cheaters_2"
   },
   "source": [
    "**Null hypothesis:** the chance of winning is 50% of winning.\n",
    "\n",
    "**Alternative hypothesis:** the chance of winning is higher than 50% of winning. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"hide\">\\pagebreak</div>\n",
    "\n",
    "**Question 3.** Given the outcome of 20 games, which of the following test statistics would be a reasonable choice for this hypothesis test?\n",
    "\n",
    "1. Whether there is at least one win.\n",
    "1. Whether there is at least one loss.\n",
    "1. The number of wins.\n",
    "1. The number of wins minus the number of losses.\n",
    "1. The total variation distance between the probability distribution of a fair coin and the observed distribution of heads and tails.\n",
    "1. The total amount of money that the customer won.\n",
    "\n",
    "Assign `reasonable_test_statistics` to a **list** of numbers corresponding to these test statistics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3, 4, 6]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reasonable_test_statistics = list(make_array(3,4,6))\n",
    "reasonable_test_statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Running tests\n",
      "\n",
      "---------------------------------------------------------------------\n",
      "Test summary\n",
      "    Passed: 1\n",
      "    Failed: 0\n",
      "[ooooooooook] 100.0% passed\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = ok.grade('q1_3')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"hide\">\\pagebreak</div>\n",
    "**Question 4.** Write a function called `simulate`.  It should take no arguments.  It should return the number of wins in 20 games simulated under the assumption that the result of each game is sampled from a fair coin."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def simulate():\n",
    "    n = 20\n",
    "    result = make_array('Win', 'Lose')\n",
    "    sample = np.random.choice(result, n)\n",
    "    win = np.count_nonzero(sample == 'Win')\n",
    "    return win\n",
    "simulate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Running tests\n",
      "\n",
      "---------------------------------------------------------------------\n",
      "Test summary\n",
      "    Passed: 1\n",
      "    Failed: 0\n",
      "[ooooooooook] 100.0% passed\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = ok.grade('q1_4')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 5.** Using a 10,000 trial simulation, generate a histogram of the empirical distribution of the number of wins in 20 games."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "deletable": false,
    "for_assignment_type": "student",
    "manual_grade": true,
    "manual_problem_id": "catching_cheaters_5"
   },
   "outputs": [
    {
     "data": {
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Dhw7F9evXVbbt2LEjbt++XeXmEuB5r04kEiEpKQkPHz5UCj5/f388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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f855682d080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 10000\n",
    "\n",
    "sampled_stats = make_array()\n",
    "bet = make_array('Win', 'Lose')\n",
    "\n",
    "\n",
    "for i in np.arange(n):\n",
    "    new_sample = np.random.choice(bet, 20)\n",
    "    win = np.count_nonzero(new_sample == 'Win')\n",
    "    sampled_stats = np.append(sampled_stats, win)\n",
    "    \n",
    "results = Table().with_column('10,000 Trials', sampled_stats)\n",
    "results.hist( '10,000 Trials', bins = np.arange(1,21,1), unit = 'Win')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"hide\">\\pagebreak</div>\n",
    "\n",
    "**Question 6.** Compute an empirical P-value for this test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1258"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "p_value = np.count_nonzero(sampled_stats >= 13)/n\n",
    "p_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "for_assignment_type": "student"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Running tests\n",
      "\n",
      "---------------------------------------------------------------------\n",
      "Test summary\n",
      "    Passed: 1\n",
      "    Failed: 0\n",
      "[ooooooooook] 100.0% passed\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = ok.grade('q1_6')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"hide\">\\pagebreak</div>\n",
    "#### Question 7\n",
    "Suppose you use a P-value cutoff of 1%, according to the arbitrary conventions of hypothesis testing.  What do you conclude?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "manual_grade": true,
    "manual_problem_id": "catching_cheaters_7"
   },
   "source": [
    "*null hypothesis is correct*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"hide\">\\pagebreak</div>\n",
    "#### Question 8\n",
    "Is `p_value` the probability that the customer cheated, or the probability that the customer didn't cheat, or neither?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "manual_grade": true,
    "manual_problem_id": "catching_cheaters_8"
   },
   "source": [
    "*neither since we got the p_value from the experiment and assumed that null hypothesis is true*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"hide\">\\pagebreak</div>\n",
    "#### Question 9\n",
    "Is 1% (the P-value cutoff) the probability that the customer cheated, or the probability that the customer didn't cheat, or neither?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "manual_grade": true,
    "manual_problem_id": "catching_cheaters_9"
   },
   "source": [
    "*the probability that the customer cheated*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"hide\">\\pagebreak</div>\n",
    "**Question 10**\n",
    "\n",
    "Suppose you run this test for 400 different customers after observing each customer play 20 games.  When you reject the null hypothesis for a customer, you accuse that customer of cheating.  If no customer were actually cheating, how many would you expect to accuse, on average (if any)?  Assume a 1% P-value cutoff. Explain your answer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Since we're using 1% p_value cutoff, 40 customers are expected to be accused on average.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Landing a Spacecraft\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Note: This problem describes something that's close to [a real story with a very exciting video](http://www.space.com/29119-spacex-reusable-rocket-landing-crash-video.html), but the details have been changed somewhat.)\n",
    "\n",
    "SpaceY, a company that builds and tests spacecraft, is testing a new reusable launch system.  Most spacecraft use a \"first stage\" rocket that propels a smaller payload craft away from Earth, then falls back to the ground and crashes.  SpaceY's new system is designed to land safely at a landing pad at a certain location, ready for later reuse.  If it doesn't land in the right location, it crashes, and the (very expensive) vehicle is destroyed.\n",
    "\n",
    "SpaceY has tested this system over 1000 times.  Ordinarily, the vehicle doesn't land exactly on the landing pad.  For example, a gust of wind might move it by a few meters just before it lands.  It's reasonable to think of these small errors as random.  That is, the landing locations are drawn from some distribution over locations on the surface of Earth, centered around the landing pad.\n",
    "\n",
    "Run the next cell to see a plot of those locations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mti4iMYNo1JhSJWVBEOY/c17krFu3jh/84Ac0NDTQ19fH008/zbXXXsvu3bvp7u4GoLy8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\ncoiIiCgqMcghIiKiqMQgh4iIiKLS/weadUP+0aSobwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbbff8c72e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ordinary_landing_spots = Table.read_table(\"ordinary_landing_spots.csv\")\n",
    "ordinary_landing_spots.scatter(\"x\", label=\"Landing locations\")\n",
    "plots.scatter(0, 0, c=\"w\", s=1000, marker=\"*\", label=\"Landing pad\")\n",
    "plots.legend(scatterpoints=1, bbox_to_anchor=(1.6, .5));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "During one test, the vehicle lands far away from the landing pad and crashes.  SpaceY investigators suspect there was a problem unique to this landing, a problem that wasn't part of the ordinary pattern of variation in landing locations.  They think a software error in the guidance system caused the craft to incorrectly attempt to land at a spot other than the landing pad.  The guidance system engineers think there was nothing out of the ordinary in this landing, and that there was no special problem with the guidance system.\n",
    "\n",
    "Run the cell below to see a plot of the 1100 ordinary landings and the crash."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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W21Ou19LexcG64/h6enG7nMyvmMPsovzEc6+8vofOLj9hPYLTqUbnWqkqPn8g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hAAAg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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbbb6070a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "landing_spot = make_array(80.59, 30.91)\n",
    "ordinary_landing_spots.scatter(\"x\", label=\"Other landings\")\n",
    "plots.scatter(0, 0, c=\"w\", s=1000, marker=\"*\", label=\"Landing pad\")\n",
    "plots.scatter(landing_spot.item(0), landing_spot.item(1), marker=\"*\", c=\"r\", s=1000, label=\"Crash site\")\n",
    "plots.legend(scatterpoints=1, bbox_to_anchor=(1.6, .5));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"hide\">\\pagebreak</div>\n",
    "#### Question 1\n",
    "Suppose we'd like to use hypothesis testing to shed light on this question.  We've written down an alternative hypothesis below.  What is a reasonable null hypothesis?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "for_assignment_type": "student"
   },
   "source": [
    "**Null hypothesis:** This landing was not special; its location was a draw from the other 1100 landing locations were drawn. \n",
    "\n",
    "**Alternative hypothesis:** This landing was special; its location was a draw from some other distribution, not the distribution from which the other 1100 landing locations were drawn."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"hide\">\\pagebreak</div>\n",
    "#### Question 2\n",
    "What's a good test statistic? (*Hint:* If we want to compare landings, we might want to see how far each landing is from some *reference point*, so we can compare all landings from the same vantage point)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "for_assignment_type": "student"
   },
   "source": [
    "**Test statistic: How far away is each landing from the landing pad? ** "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"hide\">\\pagebreak</div>\n",
    "#### Question 3\n",
    "Write a function called `landing_test_statistic`.  It should take two arguments: an \"x\" location and a \"y\" location (both numbers).  It should return the value of your test statistic for a landing at those coordinates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def landing_test_statistic(x_coordinate, y_coordinate):\n",
    "    return ((0-x_coordinate)**2+(0-y_coordinate)**2)**(1/2)\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"hide\">\\pagebreak</div>\n",
    "#### Question 4\n",
    "The cell below computes a P-value using your test statistic.  Describe the test procedure in words.  Is there a simulation involved?  If so, what is being simulated? If not, why not?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.012727272727272728"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_stat = landing_test_statistic(\n",
    "    landing_spot.item(0),\n",
    "    landing_spot.item(1))\n",
    "\n",
    "null_stats = make_array()\n",
    "for i in np.arange(ordinary_landing_spots.num_rows):\n",
    "    null_stat = landing_test_statistic(\n",
    "        ordinary_landing_spots.column('x').item(i),\n",
    "        ordinary_landing_spots.column('y').item(i))\n",
    "    null_stats = np.append(null_stats, null_stat)\n",
    "\n",
    "p_value = np.count_nonzero(null_stats > test_stat) / len(null_stats)\n",
    "p_value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Write your answer here, replacing this text.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Testing Dice\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Students in a Data Science class want to figure out whether a six-sided die is fair or not. On a fair die, each face of the die appears with chance 1/6 on each roll, regardless of the results of other rolls.  Otherwise, a die is called unfair.  We can describe a die by the probability of landing on each face.  For example, this table describes a die that is unfairly weighted toward 1:\n",
    "\n",
    "|Face|Probability|\n",
    "|--|\n",
    "|1|.5|\n",
    "|2|.1|\n",
    "|3|.1|\n",
    "|4|.1|\n",
    "|5|.1|\n",
    "|6|.1|\n",
    "\n",
    "For this exercise, you can use the function `proportion_from_distribution` defined in lecture and the textbook.  We've defined it in the setup cell above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"hide\">\\pagebreak</div>\n",
    "#### Question 1\n",
    "Define a null hypothesis and an alternative hypothesis for this question."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "for_assignment_type": "student",
    "manual_grade": true,
    "manual_problem_id": "testing_dice_1"
   },
   "source": [
    "**Null hypothesis:** each face of the die appears with chance 1/6 on each roll, regardless of the results of other rolls.\n",
    "\n",
    "**Alternative hypothesis:** each face of the die appears not equally likely on each roll, regardless of the results of other rolls."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We decide to test the die by rolling it 5 times. The proportions of the 6 faces in these 5 rolls are stored in a table with 6 rows.  For example, here is the table we'd make if the die rolls ended up being 1, 2, 3, 3, and 5:\n",
    "\n",
    "|Face|Proportion|\n",
    "|--|\n",
    "|1|.2|\n",
    "|2|.2|\n",
    "|3|.4|\n",
    "|4|.0|\n",
    "|5|.2|\n",
    "|6|.0|\n",
    "\n",
    "The function `mystery_test_statistic`, defined below, takes a single table like this as its argument and returns a number (which we will use as a test statistic)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Note: We've intentionally used obscurantist function and\n",
    "# variable names to avoid giving away answers.  It's rarely\n",
    "# a good idea to use names like \"x\" in your code.\n",
    "\n",
    "def mystery_test_statistic(sample):\n",
    "    x = sum(sample.column(\"Face\")*sample.column(\"Proportion\"))\n",
    "    y = np.mean(np.arange(1, 6+1, 1))\n",
    "    return abs(x - y)\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"hide\">\\pagebreak</div>\n",
    "#### Question 2\n",
    "Describe in English what the test statistic is.  Is it equivalent to the total variation distance between the observed face distribution and the fair die distribution?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "manual_grade": true,
    "manual_problem_id": "testing_dice_2"
   },
   "source": [
    "*According to the sample die, each face of die has a different chance of appearing, whereas the fair die has a same chance of appearing. Thus, we compare the difference between them to see if there's a difference in total variation and it turns out that it is not equivalent to the total variation distance between them.  *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `simulate_observations_and_test` takes as its argument a table describing the probability distribution of a die.  It simulates one set of 5 rolls of that die, then tests the null hypothesis about that die using our test statistic function above.  It returns `False` if it *rejects* the null hypothesis about the die, and `True` otherwise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The probability distribution table for a fair die:\n",
    "fair_die = Table().with_columns(\n",
    "        \"Face\", np.arange(1, 6+1),\n",
    "        \"Probability\", [1/6, 1/6, 1/6, 1/6, 1/6, 1/6])\n",
    "\n",
    "def simulate_observations_and_test(actual_die):\n",
    "    \"\"\"Simulates die rolls from actual_die and tests the hypothesis that the die is fair.\n",
    "    \n",
    "    Returns True if that hypothesis is accepted, and False otherwise.\"\"\"\n",
    "    sample_size = 5\n",
    "    p_value_cutoff = .2\n",
    "    num_simulations = 250\n",
    "    \n",
    "    observation_set = proportions_from_distribution(actual_die, \"Probability\", sample_size)\n",
    "    actual_statistic = mystery_test_statistic(observation_set.relabeled(\"Random Sample\", \"Proportion\"))\n",
    "    \n",
    "    simulated_statistics = make_array()\n",
    "    for _ in np.arange(num_simulations):\n",
    "        one_observation_set_under_null = proportions_from_distribution(fair_die, \"Probability\", sample_size)\n",
    "        simulated_statistic = mystery_test_statistic(one_observation_set_under_null.relabeled(\"Random Sample\", \"Proportion\"))\n",
    "        simulated_statistics = np.append(simulated_statistics, simulated_statistic)\n",
    "    p_value = np.count_nonzero(actual_statistic < simulated_statistics) / num_simulations\n",
    "    \n",
    "    return p_value >= p_value_cutoff\n",
    "\n",
    "# Calling the function to simulate a test of a fair die:\n",
    "simulate_observations_and_test(fair_die)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"hide\">\\pagebreak</div>\n",
    "#### Question 3\n",
    "By examining `simulate_observations_and_test`, compute the probability that it returns `False` when its argument is `fair_die` (which is defined above the function).  You can call the function a few times to see what it does, but **don't** perform a simulation to compute this probability.  Use your knowledge of hypothesis tests."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "probability_of_false = .2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Running tests\n",
      "\n",
      "---------------------------------------------------------------------\n",
      "Test summary\n",
      "    Passed: 1\n",
      "    Failed: 0\n",
      "[ooooooooook] 100.0% passed\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = ok.grade('q3_3')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"hide\">\\pagebreak</div>\n",
    "#### Question 4\n",
    "From the perspective of someone who wants to know the truth about the die, is it good or bad for the function to return `False` when its argument is `fair_die`?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "manual_grade": true,
    "manual_problem_id": "testing_dice_4"
   },
   "source": [
    "*bad idea because of null hypothesis*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"hide\">\\pagebreak</div>\n",
    "#### Question 5\n",
    "Verify your answer to question 3 by simulation, computing an approximate probability that `simulation_observations_and_test` returns `False`.\n",
    "\n",
    "**Note:** This will be a little slow.  300 repetitions of the simulation should suffice to get an answer that's roughly correct and should require a minute or so of computation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "for_assignment_type": "student"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.18666666666666668"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_test_simulations = 300\n",
    "result = make_array()\n",
    "for i in np.arange(num_test_simulations):\n",
    "    simulation = simulate_observations_and_test(fair_die)\n",
    "    result = np.append(result, simulation)\n",
    "    \n",
    "\n",
    "np.count_nonzero(result == False)/300\n",
    "    \n",
    "    \n",
    "\n",
    "# For reference, the staff solution involved 6 lines of code before this.\n",
    "\n",
    "approximate_probability_of_false = np.count_nonzero(result == False)/300\n",
    "approximate_probability_of_false"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Submission\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Once you're finished, select \"Save and Checkpoint\" in the File menu and then execute the `submit` cell below. The result will contain a link that you can use to check that your assignment has been submitted successfully. If you submit more than once before the deadline, we will only grade your final submission."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "IPython.notebook.save_checkpoint();"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "IPython.notebook.save_notebook();"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving notebook... Saved 'hw05.ipynb'.\n",
      "Submit... 100% complete\n",
      "Submission successful for user: kcs1992@berkeley.edu\n",
      "URL: https://okpy.org/cal/data8/fa17/hw05/submissions/gJmGBr\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = ok.submit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# For your convenience, you can run this cell to run all the tests at once!\n",
    "import os\n",
    "print(\"Running all tests...\")\n",
    "_ = [ok.grade(q[:-3]) for q in os.listdir(\"tests\") if q.startswith('q')]\n",
    "print(\"Finished running all tests.\")"
   ]
  }
 ],
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