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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# IntroStat Week 5\n",
    "\n",
    "Example: voltage drop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Enter data\n",
    "x = np.array([0.75,-0.85,4.23,2.12,3.04,0.53,-0.35,1.69,1.52,-0.42])\n",
    "n = len(x)\n",
    "print(x)\n",
    "print(n)\n",
    "plt.hist(x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute best estimate for the mean (and the standard error)\n",
    "mean_hat = x.mean()\n",
    "se_mean = x.std(ddof=1)/np.sqrt(n)\n",
    "print([mean_hat, x.std(ddof=1), se_mean])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# confidence interval for the mean:\n",
    "mu_lower = mean_hat - stats.t.ppf(0.975, df=9)*se_mean\n",
    "mu_upper = mean_hat + stats.t.ppf(0.975, df=9)*se_mean\n",
    "print([mu_lower, mu_upper])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Margin of Error:\n",
    "print(stats.t.ppf(0.975, df=9)*se_mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the null hypothesis\n",
    "mean_null_hyp = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute the \"test statistic\" from the oberserved data\n",
    "tobs = (mean_hat - mean_null_hyp) / se_mean\n",
    "print(tobs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# compare with t_0.975 from t-distribution with df = 9\n",
    "stats.t.ppf(0.975, df=n-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculate p-value\n",
    "2*stats.t.cdf(-tobs, df=n-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# You can also use the ttest_1samp funtion from scipy.stats:\n",
    "print(stats.ttest_1samp(x, popmean=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(stats.ttest_1samp(x, popmean=0).confidence_interval(confidence_level=0.95))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(stats.ttest_1samp(x, popmean=0).confidence_interval(confidence_level=0.99))"
   ]
  }
 ],
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