{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<figure>\n",
    "  <IMG SRC=\"https://raw.githubusercontent.com/mbakker7/exploratory_computing_with_python/master/tudelft_logo.png\" WIDTH=250 ALIGN=\"right\">\n",
    "</figure>\n",
    "\n",
    "# Exploratory Computing with Python\n",
    "*Developed by Mark Bakker*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Notebook 11: Distribution of the mean, hypothesis tests, and the central limit theorem\n",
    "In this notebook we first investigate the distribution of the mean of a dataset, we simulate several hypothesis tests, and finish with exploring the central limit theorem. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy.random as rnd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a dataset of 100 points. The data are drawn from a normal distribution with mean 4 and standard deviation 2. As we noticed before, the sample mean of the 100 data points almost always differs from 4. And every time we generate a new set of 100 points, the mean will be somewhat different. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean a: 3.5116046783038697\n",
      "mean a: 4.275416159643564\n",
      "mean a: 3.81383061598747\n",
      "mean a: 4.09378838538086\n",
      "mean a: 4.04083819722385\n"
     ]
    }
   ],
   "source": [
    "for i in range(5):\n",
    "    a = 2 * rnd.standard_normal(100) + 4\n",
    "    print('mean a:', np.mean(a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In fact, the mean of the dataset itself can be considered as a random variable with a distribution of its own. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sample standard deviation\n",
    "The sample standard deviation $s_n$ of a dataset of $n$ values is defined as\n",
    "\n",
    "$s_n = \\sqrt{ \\frac{1}{n-1} \\sum_{i=1}^n (x_i - \\overline{x}_n)^2 }$\n",
    "\n",
    "and can be computed with the `std` function of the `numpy` package. By default, the `std` function devides the sum by $n$ rather than by $n-1$. To divide by $n-1$, as we want for an unbiased estimate of the standard deviation, specify the keyword argument `ddof=1` in the `np.std` function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1. <a name=\"back1\"></a>Histogram of the means of datasets with 100 values\n",
    "Generate 1000 datasets each with 100 values drawn from a normal distribution with mean 4 and standard deviation 2; use a seed of 22. Compute the mean of each dataset and store them in an array of length 1000. Compute the mean of the means and the standard deviation of the means, and print them to the screen. Draw a boxplot of the means. In a separate figure, draw a histogram of the means. Make sure the vertical axis of the boxplot and the horizontal axis of the histogram extend from 3 to 5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#ex1answer\">Answers to Exercise 1</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 2. <a name=\"back2\"></a>Histogram of the means of datasets with 1000 values\n",
    "Repeat exercise 1 but now generate 1000 datasets each with 1000 values (rather than 100 values) drawn from the same normal distribution with mean 4 and standard deviation 2, and again with a seed of 22. Make sure the vertical axis of the boxplot and the horizontal axis of the histogram extend from 3 to 5, so that the graphs can be compared to the graphs you created in the previous exercise. Is the spread of the mean much smaller now as compared to the datasets consisting of only 100 values?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#ex2answer\">Answers to Exercise 2</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sample standard deviation of the sample mean\n",
    "The histogram of the means looks like the bell-shaped curve of a Normal distribution, but you may recall that it is actually a Student's $t$-distribution, also simply called a $t$-distribution. A $t$-distribution arises when estimating the mean of a normally distributed variable in situations where the sample size is relatively small and the standard deviation is unknown (as it pretty much always is in practice) and needs to be estimated from the data. \n",
    "\n",
    "The sample mean of a dataset of $n$ values is commonly written as $\\overline{x}_n$, while the sample standard deviation is written as $s_n$ (as defined above). Here, we are computing the sample standard deviation of the sample means, which we write as $\\hat{s}_n$ for a dataset of size $n$. Theoretically, the value of the sample standard deviation of the sample mean $\\hat{s}_n$ is related to the sample standard deviation as (see [here](http://en.wikipedia.org/wiki/Standard_deviation#Standard_deviation_of_the_mean))\n",
    "\n",
    "$\\hat{s}_n = s_n / \\sqrt{n}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Percentiles of $t$-distribution\n",
    "You may recall that the 90% interval around the mean for a Normally distributed variable runs from $\\mu-1.64\\sigma$ to $\\mu+1.64\\sigma$. In other words, 5% of the data is expected to lie below $\\mu-1.64\\sigma$ and 5% of the data is expected to lie above $\\mu+1.64\\sigma$. What now if you forgot it is $1.64\\sigma$ to the left and right of the mean? Or what if you want to know the value for some other percentile. You may look that up in a table in a Statistics book (or on the web), or use the percent point function `ppf`, which is part of any statistical distribution function defined in the `scipy.stats` package. The `ppf` function is the inverse of the cumulative distribution function. For example, `ppf(0.05)` returns the value of the data such that the cumulative distribution function is equal to 0.05 at the returned value. To find the 5% and 95% values, type (recall that by default the `norm` distribution has mean zero and standard deviation 1; you can specify different values with the `loc` and `scale` keyword arguments, respectively)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5% limit: -1.6448536269514729\n",
      "95% limit: 1.644853626951472\n",
      "check if it works for 5%: 0.049999999999999975\n",
      "check if it works for 95%: 0.95\n",
      "5% limit with mu=20, sig=10: 3.5514637304852705\n",
      "check: 0.049999999999999975\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "xvalue_05 = norm.ppf(0.05)\n",
    "xvalue_95 = norm.ppf(0.95)\n",
    "print('5% limit:', xvalue_05)\n",
    "print('95% limit:', xvalue_95)\n",
    "print('check if it works for 5%:', norm.cdf(xvalue_05))\n",
    "print('check if it works for 95%:', norm.cdf(xvalue_95))\n",
    "# Next, specify a mean and standard deviation\n",
    "xvalue_05_musig = norm.ppf(0.05, loc=20, scale=10) # mu = 20, sigma = 10\n",
    "print('5% limit with mu=20, sig=10:', xvalue_05_musig)\n",
    "print('check:', norm.cdf(xvalue_05_musig, loc=20, scale=10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A similar function exists for the $t$ distribution. The $t$-distribution takes one additional argument: the number of degrees of freedom, which is equal to the number of data points minus 1. For example, consider a sample with 40 data points, a sample mean of 20, and a sample standard deviation of the mean of 2, then the 5 and 95 percentiles are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5% limit:   16.63024975657755\n",
      "95% limit:  23.369750243422448\n",
      "check if it works for 5%: 0.04999999999999998\n",
      "check if it works for 95%: 0.9499999999999998\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import t\n",
    "xvalue_05 = t.ppf(0.05, 39, loc=20, scale=2)\n",
    "xvalue_95 = t.ppf(0.95, 39, loc=20, scale=2)\n",
    "print('5% limit:  ',xvalue_05)\n",
    "print('95% limit: ',xvalue_95)\n",
    "print('check if it works for 5%:', t.cdf(xvalue_05, 39, loc=20, scale=2))\n",
    "print('check if it works for 95%:', t.cdf(xvalue_95, 39, loc=20, scale=2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 3. <a name=\"back3\"></a>Count the number of means outside 95 percentile\n",
    "Go back to Exercise 1. Generate 1000 datasets each with 100 values drawn from a normal distribution with mean 4 and standard deviation 2. For each dataset, evaluate whether the sample mean is within the 95 percentile of the $t$-distribution around the true mean of 4 (the standard deviation of the sample mean is different every time, of course). Count how many times the sample mean is outside the 95 percentile around the true mean of the $t$ distribution. If the theory is correct, it should, of course, be the case for about 5% of the datasets. Try five different seeds and report the percentage of means in the dataset that is outside the 95 percentile around the true mean. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#ex3answer\">Answers to Exercise 3</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 4. <a name=\"back4\"></a>$t$ test on dataset of 20 values\n",
    "Generate 20 datapoints from a Normal distribution with mean 39 and standard deviation 4. Use a seed of 2. Compute and report the sample mean and sample standard deviation of the dataset and the sample standard deviation of the sample mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you computed it correctly, the mean of the 20 data points generated above is 38.16. Somebody now claims that the 20 datapoints are taken from a distribution with a mean of 40. You are asked to decide wether the true underlying mean could indeed be 40. In statistical terms, you are asked to perform a Hypothesis test, testing the null hypothesis that the mean is 40 against the alternative hypothesis that the mean is not 40 at significance level 5%. Hence, you are asked to do a two-sided $t$-test. All you can do in Hypothesis testing it trying to reject the null hypothesis, so let's try that. Most statistics books give a cookbook recipe for performing a $t$-test. Here we will visualize the $t$-test. We reject the null hypothesis if the sample mean is outside the 95% interval around the mean of the corresponding $t$-distribution. If the mean is inside the 95% interval we can only conclude that there is not enough evidence to reject the null hypothesis. Draw the probability density function of a $t$-distribution with mean 40 and standard deviation equal to the sample standard deviation of the sample mean you computed above. Draw red vertical lines indicating the left and right limits of the 95% interval around the mean. Draw a heavy black vertical line at the position of the sample mean you computed above. Decide whether you can reject the null hypothesis that the mean is 40 and add that as a title to the figure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#ex4answer\">Answers to Exercise 4</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 5. <a name=\"back5\"></a>Hypothesis tests on Wooden beam data\n",
    "Load the data set of experiments on wooden beams stored in the file `douglas_data.csv`. First, consider the first 20 measurements of the bending strength. Compute the sample mean and the standard deviation of the sample mean. The manufacturer claims that the mean bending strength is only 50 N/mm$^2$. Perform a $t$-test (significance level 5%) with null hypothesis that the mean is indeed 50 N/mm$^2$ and alternative hypothesis that the mean is not 50 N/mm$^2$ using the approach applied in Exercise 4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Repeat the $t$-test above but now with all the measurements of the bending strength. Do you reach the same conclusion?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#ex5answer\">Answers to Exercise 5</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Central limit theorem\n",
    "So far we looked at the distribution of the sample mean of a dataset while we knew that the data was taken from a normal distribution (except for the wooden beam data, but that looked very much like a Normal distribution). Such a sample mean has a Student $t$-distribtion, which approaches the Normal distribution when the dataset is large. Actually, 100 datapoints is already enough to approach the Normal distribution fairly closely. You may check this by comparing, for example, the percent point function `ppf` of a Normal distribution with a $t$-distribution with 99 degrees of freedom, or by simply plotting the pdf of both distributions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95 percentile Standard Normal:   1.644853626951472\n",
      "95 percentile t-dist with n=99:  1.6603911559963895\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('95 percentile Standard Normal:  ',norm.ppf(0.95))\n",
    "print('95 percentile t-dist with n=99: ',t.ppf(0.95,99)) \n",
    "x = np.linspace(-4,4,100)\n",
    "y1 = norm.pdf(x)\n",
    "y2 = t.pdf(x,99)\n",
    "plt.plot(x,y1,'b',label='Normal')\n",
    "plt.plot(x,y2,'r',label='t-dist')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Central limit theorem now states that the distribution of the sample mean approaches the Normal distribution in the limit even if the dataset is drawn from an entirely different distribution! We are going to test this theorem by drawing numbers from a Gamma distribution. The Gamma distribution is a skewed distribution and takes a shape parameter $k$ and a scale parameter $\\theta$, and is defined for $x>0$. Details on the Gamma distribution can be found, for example [here](http://en.wikipedia.org/wiki/Gamma_distribution). Let's set the shape parameter equal to 2 and the scale parameter equal to 1 (which happens to be the default). When the scale parameter is equal to 1, the mean is equal to the shape parameter. The pdf of the Gamma distribution for these values is shown below. The mean is indicated with the red vertical line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import gamma\n",
    "x = np.linspace(1e-6, 10, 100)\n",
    "y = gamma.pdf(x, 2, scale=1)\n",
    "plt.plot(x, y)\n",
    "plt.axvline(2, color='r');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Random numbers may be drawn from any distribution in the `scipy.stats` package with the `rvs` function. Here, we draw 1000 numbers and add the histogram to the previous figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(1e-6, 10, 100)\n",
    "y = gamma.pdf(x, 2)\n",
    "plt.plot(x, y)\n",
    "plt.axvline(2, color='r')\n",
    "data = gamma.rvs(2, size=1000)\n",
    "plt.hist(data, bins=20, density=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 6. <a name=\"back6\"></a>Explore Central Limit Theorem for Gamma Distribution\n",
    "Generate $N$ datasets of 20 numbers randomly drawn from a Gamma distribution with shape parameter equal to 2 and scale equal to 1. Draw a histogram of the means of the $N$ datasets using 20 bins. On the same graph, draw the pdf of the Normal distribution using the mean of means and sample standard deviation of the means; choose the limits of the $x$-axis between 0 and 4. Make 3 graphs, for $N=100,1000,10000$ and notice that the distribution starts to approach a Normal distribution. Add a title to each graph stating the number of datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#ex6answer\">Answers to Exercise 6</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Answers to the exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"ex1answer\">Answers to Exercise 1</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of the means is: 4.004742118538674\n",
      "The standard deviation of the means is: 0.1904854817672302\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(3.0, 5.0)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rnd.seed(22)\n",
    "mean_of_data = np.mean(2 * rnd.standard_normal((1000, 100)) + 4, 1)\n",
    "print('The mean of the means is:', np.mean(mean_of_data))\n",
    "print('The standard deviation of the means is:', np.std(mean_of_data, ddof=1))\n",
    "plt.figure()\n",
    "plt.boxplot(mean_of_data)\n",
    "plt.ylim(3, 5)\n",
    "plt.figure()\n",
    "plt.hist(mean_of_data, density=True)\n",
    "plt.xlim(3,5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#back1\">Back to Exercise 1</a>\n",
    "\n",
    "<a name=\"ex2answer\">Answers to Exercise 2</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of the means is: 4.001281312353626\n",
      "The standard deviation of the means is: 0.0654148250988205\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(3.0, 5.0)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rnd.seed(22)\n",
    "mean_of_data = np.mean(2 * rnd.standard_normal((1000, 1000)) + 4, 1)\n",
    "print('The mean of the means is:', np.mean(mean_of_data))\n",
    "print('The standard deviation of the means is:', np.std(mean_of_data, ddof=1))\n",
    "plt.figure()\n",
    "plt.boxplot(mean_of_data)\n",
    "plt.ylim(3,5)\n",
    "plt.figure()\n",
    "plt.hist(mean_of_data)\n",
    "plt.xlim(3, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#back2\">Back to Exercise 2</a>\n",
    "\n",
    "<a name=\"ex3answer\">Answers to Exercise 3</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "percentage of datasets where sample mean is outside 95 percentile: 4.0\n",
      "percentage of datasets where sample mean is outside 95 percentile: 5.8\n",
      "percentage of datasets where sample mean is outside 95 percentile: 6.2\n",
      "percentage of datasets where sample mean is outside 95 percentile: 5.9\n",
      "percentage of datasets where sample mean is outside 95 percentile: 5.7\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import t\n",
    "for s in [22, 32, 42, 52, 62]:\n",
    "    rnd.seed(s)\n",
    "    data = 2.0 * rnd.standard_normal((1000, 100)) + 4.0\n",
    "    mean = np.mean(data, 1)\n",
    "    sighat = np.std(data, axis=1, ddof=1) / np.sqrt(100)\n",
    "    count = 0\n",
    "    for i in range(1000):\n",
    "        low = t.ppf(0.025, 99, loc=4, scale=sighat[i])\n",
    "        high = t.ppf(0.975, 99, loc=4, scale=sighat[i])\n",
    "        if (mean[i] < low) or (mean[i] > high): count += 1\n",
    "    print('percentage of datasets where sample mean is outside 95 percentile:', count * 100 / 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#back3\">Back to Exercise 3</a>\n",
    "\n",
    "<a name=\"ex4answer\">Answers to Exercise 4</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean of the data: 38.16274004693891\n",
      "std of the data: 4.460326920868606\n",
      "std of the mean: 0.9973594196934527\n"
     ]
    }
   ],
   "source": [
    "rnd.seed(2)\n",
    "data = 4 * rnd.standard_normal(20) + 39\n",
    "mu = np.mean(data)\n",
    "sig = np.std(data, ddof=1)\n",
    "sighat = np.std(data, ddof=1) / np.sqrt(20)\n",
    "print('mean of the data:', mu)\n",
    "print('std of the data:', sig)\n",
    "print('std of the mean:', sighat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(37, 43, 100)\n",
    "y = t.pdf(x, 19, loc=40, scale=sighat)\n",
    "plt.plot(x, y)\n",
    "perc025 = t.ppf(0.025, 19, loc=40, scale=sighat)\n",
    "perc975 = t.ppf(0.975, 19, loc=40, scale=sighat)\n",
    "plt.axvline(perc025, color='r')\n",
    "plt.axvline(perc975, color='r')\n",
    "plt.axvline(mu, color='k', lw=5)\n",
    "plt.title('H0 cannot be rejected');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#back4\">Back to Exercise 4</a>\n",
    "\n",
    "<a name=\"ex5answer\">Answers to Exercise 5</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sample mean, standard deviation of sample mean:  69.37100000000001 3.5096083077295406\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pandas import read_csv\n",
    "w = read_csv('douglas_data.csv', skiprows=[1], skipinitialspace=True)\n",
    "mu20 = np.mean(w.bstrength[:20])\n",
    "sig20 = np.std(w.bstrength[:20], ddof=1) / np.sqrt(20)\n",
    "print('sample mean, standard deviation of sample mean: ', mu20, sig20)\n",
    "x = np.linspace(30,70,100)\n",
    "y = t.pdf(x, 19, loc=50, scale=sig20)\n",
    "plt.plot(x,y)\n",
    "perc025 = t.ppf(0.025, 19, loc=50, scale=sig20)\n",
    "perc975 = t.ppf(0.975, 19, loc=50, scale=sig20)\n",
    "plt.axvline(perc025, color='r')\n",
    "plt.axvline(perc975, color='r')\n",
    "plt.axvline(mu20, color='k', lw=4)\n",
    "plt.title('H0 is rejected: mean is not 50 N/mm2');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sample mean, standard deviation of sample mean:  48.65050561797753 0.9035436317023355\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pandas import read_csv\n",
    "w = read_csv('douglas_data.csv', skiprows=[1], skipinitialspace=True)\n",
    "N = len(w.bstrength)\n",
    "mu = np.mean(w.bstrength)\n",
    "sig = np.std(w.bstrength, ddof=1) / np.sqrt(N)\n",
    "print('sample mean, standard deviation of sample mean: ', mu, sig)\n",
    "x = np.linspace(30, 70, 100)\n",
    "y = t.pdf(x, N - 1, loc=50, scale=sig)\n",
    "plt.plot(x, y)\n",
    "perc025 = t.ppf(0.025, N - 1, loc=50, scale=sig)\n",
    "perc975 = t.ppf(0.975, N - 1, loc=50, scale=sig)\n",
    "plt.axvline(perc025, color='r')\n",
    "plt.axvline(perc975, color='r')\n",
    "plt.axvline(mu, color='k', lw=4)\n",
    "plt.title('Not enough evidence to reject H0: mean may very well be 50 N/mm2');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#back5\">Back to Exercise 5</a>\n",
    "\n",
    "<a name=\"ex6answer\">Answers to Exercise 6</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm, gamma\n",
    "for N in [100, 1000, 10000]:\n",
    "    data = gamma.rvs(2, size=(N, 20))\n",
    "    mean_of_data = np.mean(data, 1)\n",
    "    mu = np.mean(mean_of_data)\n",
    "    sig = np.std(mean_of_data, ddof=1)\n",
    "    plt.figure()\n",
    "    plt.hist(mean_of_data, bins=20, density=True)\n",
    "    x = np.linspace(0, 4, 100)\n",
    "    y = norm.pdf(x, loc=mu, scale=sig)\n",
    "    plt.plot(x, y, 'r')\n",
    "    plt.title('N=' + str(N))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"#back6\">Back to Exercise 6</a>"
   ]
  }
 ],
 "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": "3.13.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}