University officials hope that changes they have made have improved the retention rate. Last year, a sample of 1937 freshmen showed that 1537 returned as sophomores. This year, 1575 of 1915 freshmen sampled returned as sophomores. Determine if there is sufficient evidence at the 0.05
level to say that the retention rate has improved. Let last year's freshmen be Population 1 and let this year's freshmen 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.

Construct a confidence interval for the ratio of the two population variances using the given information. Assume the samples come from populations that are approximately normally distributed. Write your answer using interval notation, and round the interval endpoints to four decimal places.

n1=10 , n2=11, s21=7.324, s22=3.601, 95% level of confidence

A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for type I ovens is greater than the repair cost for type II ovens. A sample of 69 type I ovens has a mean repair cost of $71.66. The population standard deviation for the repair of type I ovens is known to be $24.27. A sample of 69 type II ovens has a mean repair cost of $68.79. The population standard deviation for the repair of type II ovens is known to be $13.63. Conduct a hypothesis test of the technician's claim at the 0.1 level of significance. Let μ1 be the true mean repair cost for type I ovens and μ2 be the true mean repair cost for type II ovens.

a. State the null and alternative hypotheses for the test.
b. Compute the value of the test statistic. Round your answer to two decimal places.
c. Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to two decimal places.
d. Make the decision for the hypothesis test.

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.