Professor Adams wrote a book called Improving Your Memory. The professor claims that if you follow the program outlined in the book, your memory will defi­nitely improve. Fifteen people took the professor’s course, in which the book and its program were used. On the ­first day of class, everyone took a memory exam; and on the last day, everyone took a similar exam. The paired scores for each person follow.

Use a 0.05 level of signifi­cance to test the null hypothesis that the scores are the same whether or not people have taken the course against the alternate hypothesis that the scores of people who have taken the course are higher.

(a) State the test used.

(b) Give a. State the null and alternate hypotheses.

(c) Find the sample test statistic.

(d) For the sign test, rank-sum test, and Spearman correlation coef­ficient test, fi­nd the P-value of the sample test statistic. For the runs test of randomness, ­find the critical values from Table 10 of Appendix II.

(e) Conclude the test and interpret the results in the context of the application

Last exam 225 120 115 275 85 76 114 200 99 135 170 110 216 280 78 First exam 175 110 115 200 60 85 160 190 70 110 140 10 190 200 92