Insurance Company A claims that its customers pay less, on average, than customers of its competitor, Company B. You wonder if this is true, so you decide to compare the average monthly costs of similar insurance policies from the two companies. For a random sample of 20 people who buy insurance from Company A, the mean cost is \$178 per month with a standard deviation of \$9. For 25 randomly selected customers of Company B, you find that they pay a mean of \$185 per month with a standard deviation of \$12
. Assume that the population distributions are approximately normal and the population variances are not equal.

Find the P
-value for the hypothesis test. Round your answer to four decimal places.

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.

Audrey is training for her first marathon, and she wants to know if there is a significant difference between the true mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 55 randomly selected people who train in groups and finds that they run a mean of 46.9 miles per week. Assume that the population standard deviation for the group runners is known to be 5.2 miles per week. She also interviews a random sample of 45 people who train on their own and finds that they run a mean of 49.9 miles per week. Assume that the population standard deviation for people who run by themselves is 5.7
miles per week.

Find the P
-value for the hypothesis test. Round your answer to four decimal places.
b. Is there sufficient evidence to conclude that there is a significant difference between the true mean number of miles run each week by group runners and individual runners who are training for marathons? Test the claim at the 0.01 level of significance.

Adele and Jessica live in different states and disagree about who has the higher electric bills. To settle their disagreement, the girls decide to sample electric bills in their area for the month of July and perform a hypothesis test. The electric company in Adele’s state reports that a random sample of 51 monthly residential electric bills has a mean of \$87.63. Assume that the population standard deviation in Adele's state is known to be \$22.98. For a random sample of 35 monthly residential electric bills in Jessica's state, the mean is \$84.22. Assume that the population standard deviation in Jessica's state is \$21.45. Is there evidence at the 0.01
level to say that the mean monthly residential electric bill is higher for Adele’s state than for Jessica’s state?

Find the P
-value for the hypothesis test. Round your answer to four decimal places.
b. Is there sufficient evidence to conclude that the mean monthly residential electric bill is higher for Adele's state than for Jessica's state? Test the claim at the 0.01 level of significance.