1. A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained physical activity. What sample size should be obtained if she wishes the estimate to be within three percentage points with 90% confidence, assuming that

(a) she uses the estimates of 22.7% male and 18.1% female from a previous year?

(b) she does not use any prior estimates?

2. In an experiment, 18 babies were asked to watch a climber attempt to ascend a hill. On two occasions, the baby witnesses the climber fail to make the climb. Then, the baby witnesses either a helper toy push the climber up the hill, or a hinderer toy preventing the climber from making the ascent. The toys were shown to each baby in a random fashion. A second part of this experiment showed the climber approach the helper toy, which is not a surprising action, and then the climber approached the hinderer toy, which is a surprising action. The amount of time the baby watched the event was recorded. The mean difference in time spent watching the climber approach the hinderer toy versus watching the climber approach the helper toy was 1.24 seconds with a standard deviation of 1.76 seconds. Complete parts a through c.

(b) Assuming the differences are normally distributed with no outliers, test if the difference in the amount of time the baby will watch the hinderer toy versus the helper toy is greater than 0 at the 0.01 level of significance.

Find the test statistic for this hypothesis test