A researcher collects data on the distance between college students' high schools and their colleges. He believes that the median distance is 190 miles. A random sample of 15 students yields the following number of miles between their high schools and colleges:
15 15 20 20 35 35 45 65 75 100 125 165 185 800 2160
Test the researcher's hypothesis at α = 0.05.
You may use the following abbreviated table of critical values for the sign test (two-tailed, = .05), taken from Table J in the text:
A) Reject because the test value 2 is less than the critical value 3.
B) Accept because the test value 4 is less than the critical value 13.
C) Reject because the test value 13 is more than the critical value 3.
D) Accept because the test value 190 is more than the critical value 3.

Question

A researcher collects data on the distance between college students' high schools and their colleges. He believes that the median distance is 190 miles. A random sample of 15 students yields the following number of miles between their high schools and colleges:
15 15 20 20 35 35 45 65 75 100 125 165 185 800 2160
Test the researcher's hypothesis at α = 0.05.
You may use the following abbreviated table of critical values for the sign test (two-tailed,  = .05), taken from Table J in the text: 
A) Reject because the test value 2 is less than the critical value 3. 
B) Accept because the test value 4 is less than the critical value 13. 
C) Reject because the test value 13 is more than the critical value 3. 
D) Accept because the test value 190 is more than the critical value 3.

Quizplus · Accepted Answer

To conduct a sign test, we need to first calculate the differences between each observation and the hypothesized median (190):

-15 -15 -170 -170 -155 -155 -145 -125 -115 -90 -65 -25 -5 610 1970

From this sample, we find that 2 out of the 15 observations have a distance greater than the hypothesized median (190). We use the two-tailed sign test, so our critical value from the table is 3. Since our test value (2) is less than the critical value (3), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the median distance between high schools and colleges is significantly different from 190 miles.

A Researcher Collects Data on the Distance Between College Students