Question: In Exercise 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, -2, 0, 2, 4, -3, 0, 0, 0, -2, 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 = .05. (Find the p-value, not the rejection region.)

d. Carry out the test using a = .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.

Exercise: An experiment was performed by 15 students in a statistics class at the University of California-Davis to determine whether manual dexterity was better for the dominant hand compared to the nondominant hand (left or right). Each student measured the number of beans they could place into a cup in 15 seconds, once with the dominant hand and once with the nondominant hand. The order in which the two hands were measured was randomized for each student.

a. Explain whether a comparison of beans placed using the dominant and nondominant hands is a comparison of paired data or two independent samples.

b. Referring to material earlier in the book, explain why the order of the two hands was randomized rather than, for instance, having each student test the dominant hand first.

c. The data are presented in the table below and are given also in the beans dataset. Assuming that these students represent a random sample from the population, compute a 90% confidence interval for the mean difference in the number of beans that can be placed into a cup in 15 seconds by the dominant and nondominant hands.

d. Write a sentence or two using the interval in part (c) to address the question of whether manual dexterity is better, on average, for the dominant hand.