1. A group of 51 college students from a certain liberal arts college were randomly sampled and asked about the number of alcoholic drinks they have in a typical week. The purpose of this study was to compare the drinking habits of the students at the college to the drinking habits of college students in general. In particular, the dean of students, who initiated this study, would like to check whether the mean number of alcoholic drinks that students at his college in a typical week differs from the mean of U.S. college students in general, which is estimated to be 4.73.

The group of 51 students in the study reported an average of 4.35 drinks per with a standard deviation of 3.88 drinks.

Find the p-value for the hypothesis test. _______

The p-value should be rounded to 4-decimal places.

2. Commute times in the U.S. are heavily skewed to the right. We select a random sample of 210 people from the 2000 U.S. Census who reported a non-zero commute time.

In this sample the mean commute time is 28.1 minutes with a standard deviation of 18.8 minutes. Can we conclude from this data that the mean commute time in the U.S. is less than half an hour? Conduct a hypothesis test at the 5% level of significance.

What is the p-value for this hypothesis test? _______

Your answer should be rounded to 4 decimal places.

3. Find the p-value for the hypothesis test. A random sample of size 51 is taken. The sample has a mean of 423 and a standard deviation of 84.

H0: = 400

Ha: > 400

The p-value for the hypothesis test is . _______

Your answer should be rounded to 4 decimal places.

4. In a study at West Virginia University Hospital, researchers investigated smoking behavior of cancer patients to create a program to help patients stop smoking. They published the results in Smoking Behaviors Among Cancer Survivors (January 2018, Journal of Oncology Practice). In this study, the researchers sent a 22-item survey to 995 cancer patients. They collected demographic information (age, sex, ethnicity, zip code, level of education), clinical and smoking history, and information about quitting smoking.

Of the 995 patients who were mailed surveys, 199 patients responded. For various reasons, researchers used only 179 of the completed surveys. 30 out of 94 female cancer patients reported being past smokers, and 46 out of 85 male cancer patients reported being past smokers. Calculate the difference between the corresponding sample proportions ^p1^p2 (female minus male). Round the answer to 4 decimal places. ______