10.3.
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Samples - P-Value Approach
Your friend believes that he has found a route to work that would make your commute faster than what it currently is under similar conditions. Suppose that data were collected for a random set of 7 days, where each difference is calculated by subtracting the time taken on the current route from the time taken on the new route. Assume that the populations are normally distributed. Your friend uses the alternative hypothesis \( H_{a}: \mu_{d}<0 \). Suppose the test statistic \( t \) is computed as \( t \approx-3.201 \), which has 6 degrees of freedom. What range contains the \( p \)-value?
\begin{tabular}{|l|l|l|l|l|l|}
\hline Probability & 0.10 & 0.05 & 0.025 & 0.01 & 0.005 \\
\hline Degrees of Freedom & & & & & \\
\hline 5 & 1.476 & 2.015 & 2.571 & 3.365 & 4.032 \\
\hline 6 & 1.440 & 1.943 .5 & 2.447 & 3.143 & 3.707 \\
\hline 7 & 1.415 & 1.895 & 2.365 & 2.998 & 3.499 \\
\hline 8 & 1.397 & 1.860 & 2.306 & 2.896 & 3.355 \\
\hline 9 & 1.383 & 1.833 & 2.262 & 2.821 & 3.250 \\
\hline 10 & 1.372 & 1.812 & 2.228 & 2.764 & 3.169 \\
\hline 11 & 1.363 & 1.796 & 2.201 & 2.718 & 3.106 \\
\hline 12 & 1.356 & 1.782 & 2.179 & 2.681 & 3.055 \\
\hline 13 & 1.350 & 1.771 & 2.160 & 2.650 & 3.012 \\
\hline 14 & 1.345 & 1.761 & 2.145 & 2.624 & 2.977 \\
\hline 15 & 1.341 & 1.753 & 2.131 & 2.602 & 2.947 \\
\hline
\end{tabular}
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