A researcher collects data on the distance between college students' high schools and their colleges. He believes that the median distance is 200 miles. A random sample of 15 students yields the following number of miles between their high schools and colleges: $\begin{array} { l l l l l l l l l l l l l l l } 25 & 25 & 30 & 30 & 45 & 45 & 55 & 75 & 85 & 110 & 135 & 175 & 195 & 810 & 2170 \end{array}$
Test the researcher's hypothesis at $\alpha = 0.05$.
You may use the following abbreviated table of critical values for the sign test (two-tailed $\alpha = 0.05$ ), taken from Table $J$ in the text:
$\begin{array}{l|ccccccc}
\mathbf{n} & \mathbf{1 1} & \mathbf{1 2} & \mathbf{1 3} & \mathbf{1 4} & \mathbf{1 5} & \mathbf{1 6} & \mathbf{1 7} \
\hline \text { critical value } & 1 & 2 & 2 & 3 & 3 & 3 & 4
\end{array}$
$\begin{array}{l|cccccccc}
\mathbf{n} & \mathbf{1 8} & \mathbf{1 9} & \mathbf{2 0} & \mathbf{2 1} & \mathbf{2 2} & \mathbf{2 3} & \mathbf{2 4} & \mathbf{2 5} \
\hline \text { critical value } & 4 & 4 & 5 & 5 & 5 & 6 & 6 & 6
\end{array}$
A) Reject because the test value 2 is less than the critical value 3 .
B) Reject because the test value 13 is more than the critical value 3 .
C) Accept because the test value 4 is less than the critical value 13 .
D) Accept because the test value 200 is more than the critical value 3 .

Question

Quizplus · Accepted Answer

The test value is the number of data points above or below the hypothesized median (200 miles). Here, 2 values are below 200, and 13 are above. The smaller of these is 2, which is less than the critical value of 3 for n=15. Thus, we reject the null hypothesis.