P13. C.I.E using t-values (Confidence Interval Estimate).ipynb

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   "source": [
    "# C.I.E using t-values (Confidence Interval Estimate)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "# credit card launch example\n",
    "sample mean: 1990\n",
    "sample SD: 2833\n",
    "Pop mean: ?\n",
    "n=140\n",
    "\n",
    "(In cases, where pop SD is not known, use t-values and practically in all problems prefer t over z)\n",
    "\n",
    "Q: Construct 95% confidence interval for mean card balance and interpret it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats\n",
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.977177724476122"
      ]
     },
     "execution_count": 8,
     "metadata": {},
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   ],
   "source": [
    "# t-value = stats.t.ppf(0.975,df=n-1)\n",
    "stats.t.ppf(0.975,df=139)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.977177724476122, 1.977177724476122)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
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    }
   ],
   "source": [
    "# or Simpler method : 95% t-value interval\n",
    "stats.t.interval(0.95,df=139)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "239.43220036458874"
      ]
     },
     "execution_count": 35,
     "metadata": {},
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   "source": [
    "#Sample Standard Error= Sample SD/sqrt(n) \n",
    "SE=2833/(140**0.5)\n",
    "SE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1516.642936, 2463.357064]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 95% confidence interval using t value = Sample mean -+ (t_value * SE) \n",
    "[1990-(1.977*239.432),1990+(1.977*239.432)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Or Direct Simple method: 95% CIE for Sample mean using t-value\n",
    "stats.t.interval(0.95,df,loc=samp_mean,scale=Samp_SD/Sqrt(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1516.5999869168315, 2463.4000130831682)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.t.interval(0.95,139,1990,(2833/140**0.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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