Assignment-1-Q24 (Basic Statistics Level-1).ipynb

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   "source": [
    "# Assignment-1-Q24 (Basic Statistics Level-1)"
   ]
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    "Q 24)   A Government  company claims that an average light bulb lasts 270 days. A researcher randomly selects 18 bulbs for testing. The sampled bulbs last an average of 260 days, with a standard deviation of 90 days. If the CEO's claim were true, what is the probability that 18 randomly selected bulbs would have an average life of no more than 260 days"
   ]
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  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "from scipy.stats import norm"
   ]
  },
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   "cell_type": "raw",
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   "source": [
    "Pop mean =270 days\n",
    "Sample mean = 260 days\n",
    "Sample SD = 90 days\n",
    "Sample n = 18 bulbs\n",
    "df = n-1 = 17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Assume Null Hypothesis is: Ho = Avg life of Bulb >= 260 days\n",
    "# Alternate Hypothesis is: Ha = Avg life of Bulb < 260 days"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.4714045207910317"
      ]
     },
     "execution_count": 7,
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     "output_type": "execute_result"
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   ],
   "source": [
    "# find t-scores at x=260; t=(s_mean-P_mean)/(s_SD/sqrt(n))\n",
    "t=(260-270)/(90/18**0.5)\n",
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Find P(X>=260) for null hypothesis"
   ]
  },
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   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.32167411684460556"
      ]
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     "execution_count": 5,
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   "source": [
    "# p_value=1-stats.t.cdf(abs(t_scores),df=n-1)... Using cdf function\n",
    "p_value=1-stats.t.cdf(abs(-0.4714),df=17)\n",
    "p_value"
   ]
  },
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   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.32167411684460556"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  OR p_value=stats.t.sf(abs(t_score),df=n-1)... Using sf function\n",
    "p_value=stats.t.sf(abs(-0.4714),df=17)\n",
    "p_value"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Probability that 18 randomly selected bulbs would have an average life of no more than 260 days is 32.17%"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Assuming significance value α = 0.05 (Standard Value)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "(If p_value < α ; Reject Ho and accept Ha or vice-versa)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Thus, as p-value > α ; Accept Ho i.e. The CEO claims are false and the avg life of bulb > 260 days"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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