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hypothesis_testing/hypothesis_testing.ipynb

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"\n",
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"**Step 2 — Significance level:** $\\alpha = 0.05$\n",
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"\n",
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"**Why use 7.5 million USD here?** The sample mean is around 8.4 million USD. If we test \\(H_a: \\mu > 5{,}000{,}000\\), the **t-statistic would be very large** (about 7) and the **p-value would be tiny** (about \\(10^{-12}\\)) - strong evidence, but awkward to display. Choosing \\(\\mu_0\\) closer to \\(\\bar{x}\\) keeps **t** and **p** in a familiar numeric range so you can see the decision logic clearly. The mechanics are the same for any \\(\\mu_0\\)."
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"**Why use 7.5 million USD here?** The sample mean is around 8.4 million USD. If we test $H_a: \\mu > 5{,}000{,}000$, the **t-statistic would be very large** (about 7) and the **p-value would be tiny** (about $10^{-12}$) - strong evidence, but awkward to display. Choosing $\\mu_0$ closer to $\\bar{x}$ keeps **t** and **p** in a familiar numeric range so you can see the decision logic clearly. The mechanics are the same for any $\\mu_0$."
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{

hypothesis_testing/hypothesis_testing_instructor.ipynb

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"\n",
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"**Step 2 — Significance level:** $\\alpha = 0.05$\n",
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"\n",
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"**Why use 7.5 million USD here?** The sample mean is around 8.4 million USD. If we test \\(H_a: \\mu > 5{,}000{,}000\\), the **t-statistic would be very large** (about 7) and the **p-value would be tiny** (about \\(10^{-12}\\)) - strong evidence, but awkward to display. Choosing \\(\\mu_0\\) closer to \\(\\bar{x}\\) keeps **t** and **p** in a familiar numeric range so you can see the decision logic clearly. The mechanics are the same for any \\(\\mu_0\\)."
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"**Why use 7.5 million USD here?** The sample mean is around 8.4 million USD. If we test $H_a: \\mu > 5{,}000{,}000$, the **t-statistic would be very large** (about 7) and the **p-value would be tiny** (about $10^{-12}$) - strong evidence, but awkward to display. Choosing $\\mu_0$ closer to $\\bar{x}$ keeps **t** and **p** in a familiar numeric range so you can see the decision logic clearly. The mechanics are the same for any $\\mu_0$."
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"np.float64(0.9764691345103486)"
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]
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},
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"execution_count": 30,
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"execution_count": null,
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"metadata": {},
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"output_type": "execute_result"
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}

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