A Hollywood studio believes that a movie that is considered a drama will draw a larger crowd on average than a movie that is considered a comedy. To test this theory, the studio randomly selects several movies that are classified as dramas and several movies that are classified as comedies and determines the box office revenue for each movie. The results of the survey are as follows. Assume that the population variances are approximately equal.
Box Office Revenues (Millions of Dollars)

n    x¯    s

Drama 12 140 60
Comedy 19 110 40

Calculate a 95% confidence interval for the difference in mean revenue at the box office for drama and comedy movies. Let dramas be Population 1 and comedies be Population 2. Write your answer using interval notation and round the interval endpoints to two decimal places.

Sarah believes that completely cutting caffeine out of a person’s diet will allow him or her more restful sleep at night. In fact, she believes that, on average, adults will have more than two additional nights of restful sleep in a four-week period after removing caffeine from their diets. She randomly selects 8 adults to help her test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days, and then cut back to no caffeinated beverages for the following 28 days. During each period, the participants record the numbers of nights of restful sleep that they had. The following table gives the results of the study. Test Sarah’s claim at the 0.10 level of significance assuming that the population distribution of the paired differences is approximately normal. Let the period before removing caffeine be Population 1 and let the period after removing caffeine be Population 2.

Numbers of Nights of Restful Sleep in a Four-Week Period
With Caffeine 16 15 21 22 20 21 19 19
Without Caffeine 20 19 23 24 25 25 21 18

a. State the null and alternative hypotheses for the test. Fill in the blank below.
b. Compute the value of the test statistic. Round your answer to three decimal places.
c. Draw a conclusion and interpret the decision.

A study was performed to determine the percentage of people who wear life vests while out on the water. A researcher believed that the percentage was different for those who rode jet skis compared to those who were in boats. Out of 300 randomly selected people who rode a jet ski, 91% wore life vests. Out of 350 randomly selected boaters, 84% wore life vests. Using a 0.02
level of significance, test the claim that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat. Let jet skiers be Population 1 and let boaters be Population 2.

a. State the null and alternative hypotheses for the test. Fill in the blank below.
b. Compute the value of the test statistic. Round your answer to two decimal places.
c. Make the decision and state the conclusion in terms of the original question.

A college professor is concerned that the two sections of chemistry that he teaches are not performing at the same level. To test his claim, he looks at the mean exam score for a random sample of students from each of his classes. In Class 1, the mean exam score for 18 students is 80.8 with a standard deviation of 3.8. In Class 2, the mean exam score for 23 students is 76.5 with a standard deviation of 8.8
. Assume that the population distributions are approximately normal and the population variances are equal.

Find the P
-value for the hypothesis test. Round your answer to four decimal places.
b. Is there sufficient evidence to conclude that the two sections he teaches are not performing at the same level? Test the claim at the 0.10 level of significance.

Major television networks conducted a joint poll of viewers and asked them if they felt that beer and other alcoholic beverage commercials targeted teenagers and young adults (those under 21 years old). The results of the survey are as follows.

Network Advertising Survey
Age Group Number Surveyed Number of "Yes" Responses
30 or Younger 1000 471
Older than 30 1000 515

Calculate a 90% confidence interval for the difference in the proportions of those older than 30 and those 30 or younger that believe alcoholic beverage commercials targeted teenagers and young adults. Let the 30 or younger age group be Population 1 and let the older than 30 age group be Population 2. Write your answer using interval notation and round the interval endpoints to three decimal places.