It is believed that children can throw a ball further after lunch than before lunch. A researcher decided to investigate this hypothesis using the paired-sample sign test. Each of 14 children threw a ball as far as they could before and after lunch. The distances in meters are tabulated below. Test the researcher's hypothesis at α = 0.05.
You may use the following abbreviated table of critical values for the sign test (one tailed, = .05), taken from Table J in the text:
A) The data supports the claim (rejects null hypothesis) because the test value 6 is more than the critical value 5.
B) The data does not support the claim (does not reject the null hypothesis) because the test value 4 is more than the critical value 3.
C) The data does not support the claim (does not reject the null hypothesis) because the test value 4 is less than the critical value 10.
D) The data does not support the claim (does not reject the null hypothesis) because the test value 6 is equal to the critical value 6.

Question

It is believed that children can throw a ball further after lunch than before lunch. A researcher decided to investigate this hypothesis using the paired-sample sign test. Each of 14 children threw a ball as far as they could before and after lunch. The distances in meters are tabulated below.   Test the researcher's hypothesis at α = 0.05.
You may use the following abbreviated table of critical values for the sign test (one tailed,  = .05), taken from Table J in the text: 
A) The data supports the claim (rejects null hypothesis) because the test value 6 is more than the critical value 5. 
B) The data does not support the claim (does not reject the null hypothesis) because the test value 4 is more than the critical value 3. 
C) The data does not support the claim (does not reject the null hypothesis) because the test value 4 is less than the critical value 10. 
D) The data does not support the claim (does not reject the null hypothesis) because the test value 6 is equal to the critical value 6.

Quizplus · Accepted Answer

We need to calculate the test value, which is the number of pairs where the "after lunch" distance is greater than the "before lunch" distance. In this case, there are 4 such pairs (out of 14 total pairs). Using the abbreviated table of critical values for the sign test, with n = 14 and α = 0.05, we see that the critical value is 3. Since the test value (4) is greater than the critical value (3), we cannot reject the null hypothesis that there is no significant difference between the distances children can throw a ball before and after lunch. Therefore, the data does not support the researcher's hypothesis.

It Is Believed That Children Can Throw a Ball Further