Confidence interval with the right pivot

MediumStatistics~4m

From $n=25$ daily P&L observations you get a sample mean of $50k and a sample standard deviation $s=10\text{k}$ . The population standard deviation is unknown. Build a 95% confidence interval for the true mean daily P&L and report its half-width (in $k, to two decimals). Use $t_{0.025,\,24}=2.064$ .

Show hints (2)+

$\sigma$ unknown + small $n$ $\Rightarrow$ use $t_{n-1}$ , not the Normal $1.96$ .
Half-width $=t_{0.025,24}\cdot s/\sqrt n$ .

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4.13 (± 0.02)

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Confidence interval with the right pivot

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