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.

An SAT prep course claims to improve the test score of students. The table below shows the scores for seven students the first two times they took the verbal SAT. Before taking the SAT for the second time, each student took a course to try to improve his or her verbal SAT scores. Do these results support the claim that the SAT prep course improves the students' verbal SAT scores?
Let d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course)
. Use a significance level of α=0.05 for the test. Assume that the verbal SAT scores are normally distributed for the population of students both before and after taking the SAT prep course.
Student Score on first SAT Score on second SAT
1 380 420
2 440 530
3 470 530
4 490 550
5 440 460
6 420 490
7 410 430

a. State the null and alternative hypotheses for the test.
b. Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.
c. Compute the value of the test statistic. Round your answer to three decimal places.
d. Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.
e. Make the decision for the hypothesis test.

A standardized test is given to a sixth grade class. Historically the mean score has been 173 with a variance of 30. The superintendent believes that the variance of performance may have recently increased. She randomly sampled 22 students and found a mean of 163 with a standard deviation of 5.9018. Is there evidence that the standard deviation has increased at the α=0.01 level?
State the hypotheses in terms of the standard deviation. Round the standard deviation to four decimal places when necessary.
b. Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.
c. Determine the value of the test statistic. Round your answer to three decimal places.
d. Make the decision.
e. What is the conclusion?