30. Each of a random sample of ten college freshmen takes a mathematics aptitude test both before and after undergoing an intensive training course designed to improve such test scores Then, the scores for each student are paired, as shown in Table 7.14. TABLE 7.14 Student Before After 1 60 70 2 73 80 3 42 40 4 88 94 5 66 79 6 77 86 7 90 93 8 63 71 9 55 70 10 96 97

a) Compare the mean scores after and before the training course by (i) finding the differ- cnce of the sample means, (ii) finding the mean of the difference scores. Compare

b) Calculate and interpret the P-value for testing whether the mean change equals 0.

e) Compare the mean scores after and before the training course by construcung and in- terpreting a 90% confidence interval for the population mean difference.

d) Explain the correspondence between the result of the significance test and the result of the confidence interval. What assumptions does each infercnce make?