The director for Weight Watchers International wants to determine if the changes in their program results ...

     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 your conclusion.        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