13.38 In Exercise 11.80 a study was reported in which students were asked to place as many dried beans into a cup as possible in 15 seconds with their dominant hand, and again with their nondominant hand (in randomized order). The differences in number of beans (dominant hand–nondominant hand) for 15 students were as follows:

4, 4, 5, 1, 22, 0, 2, 4, 23, 0, 0, 0, 22, 2, 1 The data also are given in the dataset beans on the companion website.

a. The research question was whether students have better manual dexterity with their dominant hand than with their nondominant hand. Write the null and alternative hypotheses.

b. Check the necessary conditions for doing a one sample t-test.

c. Carry out the test using a 5 .05. (Find the p-value, not the rejection region.)

d. Carry out the test using a 5 .10. (Find the p-value, not the rejection region.)

e. Write a conclusion about this situation that would be understood by other students of statistics.