. The director for Weight Watchers International wants to determine if the changes in their program results in better weight loss. She selected 25 Weight Watcher members at random and compared their weight 6 months later to weight at the start of the program. Here are the results: (The weight in the column labeled After represents their weights six months later and Before represents their weight at the start of the six-month period.) The director used .05 as the significance level.

Use Excel to test H0: After Before 0 vs. HA: After Before < 0. For each paired difference, compute After Before. In Data Analysis, t-Test: Paired Two Sample for means, select the After data for Variable 1 Range. Note that the critical value output by Data Analysis for this test is always positive. In this problem, the sign of the critical value is negative corresponding to a 1-tailed test with lower reject region and negative lower critical value.

• State the hypotheses.
• State the decision rule.
• Compute the test statistic
• What is your conclusion?
• What is the p-value. What does it mean?

Person	Before	After
1	176	164
2	192	191
3	185	176
4	177	176
5	196	185
6	178	169
7	196	196
8	181	172
9	158	158
10	201	193
11	191	185
12	193	189
13	176	175
14	212	210
15	177	173
16	183	180
17	210	204
18	198	192
19	157	152
20	213	200
21	161	161
22	177	166
23	210	203
24	192	186
25	178	170