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.

A golf pro believes that the variances of his driving distances are different for different brands of golf balls. In particular, he believes that his driving distances, measured in yards, have a smaller variance when he uses Titleist golf balls than when he uses a generic store brand. He hits 10 Titleist golf balls and records a sample variance of 150.43. He hits 13 generic golf balls and records a sample variance of 339.72. Assume that both population distributions are approximately normal and test the golf pro’s claim using a 0.05
level of significance. Does the evidence support the golf pro’s claim? Let the pro’s driving distances using Titleist golf balls be Population 1 and let the pro’s driving distances using generic store brand golf balls be Population 2.
State the null and alternative hypotheses for the test. Fill in the blank below.

H0Ha: σ21=σ22: σ21 ?= σ22
c. Draw a conclusion and interpret the decision.

A study was designed to compare the attitudes of two groups of nursing students towards computers. Group 1 had previously taken a statistical methods course that involved significant computer interaction. Group 2 had taken a statistic methods course that did not use computers. The students' attitudes were measured by administering the Computer Anxiety Rating Scale (CARS). A random sample of 11 nursing students from Group 1 resulted in a mean score of 40.8 with a standard deviation of 5.4. A random sample of 13 nursing students from Group 2 resulted in a mean score of 54.5 with a standard deviation of 2.3. Can you conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2? Let μ1 represent the mean score for Group 1 and μ2 represent the mean score for Group 2. Use a significance level of α=0.01

for the test. Assume that the population variances are equal and that the two populations are normally distributed.

a. State the null and alternative hypotheses for the test.
b. Compute the value of the t test statistic. Round your answer to three decimal places.
c. Determine the decision rule for rejecting the null hypothesis H0. Round your answer to three decimal places.
d. State the test's conclusion.

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.