An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 199 brakes using Compound 1 yields an average brake life of 47,673 miles. A sample of 157 brakes using Compound 2 yields an average brake life of 48,245 miles. Assume the standard deviation of brake life is known to be 3815 miles for brakes made with Compound 1 and 1538 miles for brakes made with Compound 2. Determine the 80%

confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.

a. Find the critical value that should be used in constructing the confidence interval.
b. Construct the 80% confidence interval. Round your answers to the nearest whole number.

Eddie Clauer sells a wide variety of outdoor equipment and clothing. The company sells both through mail order and via the internet. Random samples of sales receipts were studied for mail order sales and internet sales, with the total purchase being recorded for each sale. A random sample of 11 sales receipts for mail order sales results in a mean sale amount of \$93.90 with a standard deviation of \$16.25. A random sample of 15 sales receipts for internet sales results in a mean sale amount of \$86.60 with a standard deviation of \$21.25. Using this data, find the 98%

confidence interval for the true mean difference between the mean amount of mail order purchases and the mean amount of internet purchases. Assume that the population variances are not equal and that the two populations are normally distributed.

Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
b. Find the standard error of the sampling distribution to be used in constructing the confidence interval. Round your answer to two decimal places.
c. Construct the 98% confidence interval. Round your answers to two decimal places.

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.

A newspaper story claims that more houses are purchased by singles now than singles 5 years ago. To test this claim, two studies were conducted on the buying habits of singles over the past 5 years. In the first study, 500 house purchases in the current year were randomly selected and 150 of those were made by singles. In the second study, again 500 house purchases were randomly selected from 5 years ago and 117 of those were made by single people. Test the newspaper’s claim using a 0.05 level of significance. Is there sufficient evidence to support the newspaper’s claim? Let singles now be Population 1 and let singles 5
years ago be Population 2.
Answer the following questions.
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.

Major television networks conducted a joint poll of viewers and asked them if they felt that beer and other alcoholic beverage commercials targeted teenagers and young adults (those under 21 years old). The results of the survey are as follows. Based on the data, can the networks conclude that the percentage of viewers who believe beer and alcoholic beverage commercials target teenagers and young adults is significantly higher in the over 30 age group than in the 30 or younger age group at α=0.01? Let the 30 or younger age group be Population 1 and let the older than 30 age group be Population 2.