## 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

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

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 golf pro believes that the variances of his driving distances are different for different brands of golf balls

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

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 college professor is concerned that the two sections of chemistry that he teaches are not performing at the same level

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.