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Problem 6. At a high school, five boys and five girls were randomly selected from a gym class and they were paired such that each pair consisted of a boy and a girl of comparable overall physical fitness. They were then asked to do as many push-ups as they could. The following table summarizes the results for the five years. Boys 18 22 30 16 25 Girls 24 18 25 20 18 a) Create a 90% confidence interval for how many more push-ups boys can do than girls, on average, at that high school. (3 points) b) Do the sample data suggest that, on average, boys can do more push-ups than girls? Do a hypothesis test at a significance level of 0.01. (3 Points) c) List the underlying assumptions. (1 Point)