For questions (1)-(3),

• explain whether the data are one sample, matched pairs, or two samples
• articulate the null hypothesis and the alternative hypothesis
• carry out the hypothesis test at a significance level of 5 percent

1. Suppose that the average high school student watches 24.3 hours of television per week. Are Academy students like the national average? Suppose that we take a sample of 9 students at the Academy. On average, they watch 19.6 hours a week of TV with a sample standard deviation, s, of 12 hours.

2. Next, we want to know whether JDS students watch the same amount of TV as Academy students. Suppose that we take one person of each gender from each high school grade (9-12) at the Academy and one person of each gender from each high school grade at JDS. We look at the difference in TV watching. We get 8 data points in our sample. The first data point is the amount of TV the JDS freshman girl watches minus the amount that the Academy girl watches. The second data point is the amount of TV the JDS freshman boy watches minus the amount that the Academy boy watches. etc.

   Suppose that the mean difference is 0.8 hours with a sample standard deviation of 1.25 hours.

3. Instead, suppose we take a random sample of 11 JDS students and find that they watch an average of 20.3 hours of television per week, with a sample standard deviation of 10.6 hours. The question is whether they watch more TV than Academy students, where a random sample of 9 students watches an average of 19.6 hours a week of TV with a standard deviation of 12 hours.

4. Suppose that a web site is trying to provide sponsors with an estimate of unique visitors per month. It has six months of data, as follows:
   4.7 million
   5.1 million
   4.2 million
   4.9 million
   4.8 million
   4.6 million

   Calculate a 95 percent confidence interval for the number of unique visitors per month.

5. A parent alleges that half of the teachers at the Academy do not take attendance regularly. We take a random sample of 33 teachers at the Academy, and it turns out that 14 of them do not take attendance regularly. Can we reject the parent's hypothesis at a 5 percent significance level?