2. The primary advantage of a repeated-measures design over an independent- measures design is that the repeated-measures study eliminates variability due to individual differences. This usually results in smaller variability and produces a smaller standard error which increases the likelihood of a significant difference.
4. a. An independent-measures design would require two separate samples, each with 10 subjects, for a total of 20 subjects.
b. A repeated-measures design would use the same sample of n = 10 subjects in both treatment conditions.
c. A matched-subjects design would require two separate samples with n = 10 in each, for a total of 20 subjects.
6. The null hypothesis says that there is no difference between the two types of words, Ho: mean of differences = 0. With alpha equal .01, the critical region consists of t values beyond pluse/minus 2.750. For these data, s-squared = 16, the standard error is .67, and t(35) = 9.40. Reject Ho and conclude that there has been a significant difference in recall for pleasant versus unpleasant words.
8. a. For experiment 1, the mean difference = 5 and s = .82. For experiment 2, the mean difference is equal to 5 and s = 9.20.
b. For experiment 1, the standard error is .41 and t(3) = 12.20. This is beyond the critical value (t = plus/minus 3.182), so we reject Ho and conclude that the treatment has a significant effect. For experiment 2, the standard error is 4.6 and t(3) = 1.09. This is not in the critical region, so we fail to reject Ho and conclude that the treatment does not have a significant effect.
c. The consistent treatment effect in experiment 1 produces small variability and a small standard error. In experiment 2, the inconsistent results produce large variability and a large standard error.
10. The null hypothesis says that there is no increase in pain tolerance, Ho: mean difference less than or equal to 0. For a one-tailed test with alpha = .01 the critical region consistes of t values greater than 2.602. For these data, s-squared = 64, the standard error is 2, and t(15) = 5.25. Reject Ho and conclude that there has been a significant increase in pain tolerance.
12. The null hypothesis says that the drug has no effect on pain threshold, Ho: mean difference less than or equal to 0. With alpha = .05 the one-tailed critical region consists of t values greater than 1.860. For these data, s-squared = 4, the standard error is .13, and t(8) = 12.31. Reject Ho and conclude that there has been a significant change.
14. The null hypothesis says that there is no increase in gas mileage, Ho: mean difference less than or equal to 0. For a one-tailed test with alpha = .05 the critical region consists of t values greater than 1.833. For these data the standard error is .44 and t(9) = 6.14. Reject Ho and conclude that there has been a significant increase in mileage.
16. The null hypothesis says that there is no difference between shots fired during versus between heart beats, Ho: mean difference = 0. With alpha = .05 the critical region consists of t values beyond plus/minus 2.571. For these data, the mean difference = 2.83, SS = 34.83, s-squared = 6.97, the standard error is 1.08, and t(5) = 2.62. Reject Ho and conclude that the timing of the shot has a significant effect on the marksmen's scores.
18. The null hypothesis says that stress has no effect on lymphocyte count, Ho: mean difference = 0. With alpha = .05 the critical region consists of t values beyond plus/minus 2.093. For these data, the standard error is .018, and t(19) = 5.00. Reject Ho and conclude that the data show a significant change in lymphocyte count.
20. The null hypothesis says that there is no difference between the two stores, Ho: mean difference = 0. With alpha = .05 the critical region consists of t values beyond plus/minus 2.306. For these data, the mean difference = -.08, SS = .1334, s-squared = .-167, the standard error is .043, and t(8) = 1.86. Fail to reject Ho and conclude that the data show no significant difference in prices between the two stores.