1. At Rachel's 11^th birthday party, 8 girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis at the 5% level.

Relaxed time (seconds)	Jumping time (seconds)
28	20
45	43
29	25
22	21
23	25
45	43
37	35
29	32

NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

(i)State the distribution to use for the test. (Enter your answer in the form z or t_df where df is the degrees of freedom.)

(ii)What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)

(iii)What is the p-value? (Round your answer to four decimal places.) 2. At Rachel's 11^th birthday party, 8 girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis at the 5% level.

Relaxed time (seconds)	Jumping time (seconds)
26	21
45	43
29	29
22	21
23	25
45	43
37	35
29	32

(i)What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)

3. One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement, "I'm pleased with the way we divide the responsibilities for childcare." The ratings went from 1 (strongly agree) to 5 (strongly disagree). The table below contains ten of the paired responses for husbands and wives. Conduct a hypothesis test at the 5% level to see if the mean difference in the husband's versus the wife's satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife).

Wife's score	3	3	3	3	4	2	1	1	2	4
Husband's score	3	3	1	3	2	1	1	1	2	4

(i)What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.) (ii)What is the p-value? (Round your answer to four decimal places.)

4. A new SAT study course is tested on 12 individuals. Pre-course and post-course scores are recorded. Of interest is the average increase in SAT scores. The following data is collected. Conduct a hypothesis test at the 5% level.

Pre-course score	Post-course score
1200	1330
970	950
1000	1110
840	880
1100	1070
1250	1320
860	860
1330	1370
790	770
990	1040
1110	1200
740	850

(i)State the distribution to use for the test. (Enter your answer in the form z or t_df where df is the degrees of freedom.)

(ii)What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)

(iii)What is the p-value? (Round your answer to four decimal places.)