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.

Students at a major university believe they can save money buying textbooks online rather than at the local bookstores. In order to test this theory, they randomly sampled 25 textbooks on the shelves of the local bookstores. The students then found the "best" available price for the same textbooks via online retailers. The prices for the textbooks are listed in the following table. Based on the data, is it less expensive for the students to purchase textbooks from the online retailers than from local bookstores? Use α=0.01. Let prices at local bookstores represent Population 1 and prices at online retailers represent Population 2.

Textbook Prices (Dollars)
Textbook Bookstore Online Retailer Textbook Bookstore Online Retailer
1 111 89 14 91 81
2 86 62 15 96 82
3 132 112 16 98 110
4 54 49 17 139 143
5 78 72 18 99 76
6 148 143 19 135 125
7 127 138 20 62 77
8 56 52 21 133 127
9 104 110 22 100 109
10 101 80 23 77 71
11 108 118 24 54 66
12 62 44 25 85 78
13 56 35

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. Make the decision and state the conclusion in terms of the original question.
d.

Adrian hopes that his new training methods have improved his batting average. Before starting his new regimen, he was batting 0.250 in a random sample of 56 at bats. For a random sample of 25 at bats since changing his training techniques, his batting average is 0.440. Determine if there is sufficient evidence to say that his batting average has improved at the 0.02
level of significance. Let the results before starting the new regimen be Population 1 and let the results after the training 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 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. Do the data substantiate the studio's belief that dramas will draw a larger crowd on average than comedies at α=0.01? Let dramas be Population 1 and comedies be Population 2. Assume that the population variances are approximately equal.
Box Office Revenues (Millions of Dollars)

n    x¯    s

Drama 15 180 60
Comedy 13 140 20

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. Make the decision and state the conclusion in terms of the original question.

The Dodge Reports are used by many companies in the construction field to estimate the time required to complete various jobs. The company managers want to know if the time required to install 130 square feet of bathroom tile is different from the nine hours reported in the current manual. A researcher for Dodge randomly selects 54 construction workers and determines the time required to install 130 square feet of bath tile. The average time required to install the tile for the sample is 8.1 hours with a standard deviation of 3.8 hours. Use a hypothesis test to determine whether the managers’ assumptions are substantiated by the data. Use a significance level of α=0.01
. Assume the population of tile installation times is approximately normally distributed.
State the null and alternative hypotheses for the test. Fill in the blank below.

H0Ha: μ=9: μblank9
b. Compute the value of the test statistic. Round your answer to three decimal places.
c. Draw a conclusion and interpret the decision.