Testing Hypotheses: Two Sample Tests

A group of clinical physicians is performing tests on patients to determine the effectiveness of a new antihypertensive drug. Patients with high blood pressure were randomly chosen and then randomly assigned to either the control group (which received a well-established antihypertensive) or the treatment group (which received the new drug). The doctors noted the percentage of patients whose blood pressure was reduced to a normal level within 1 year. At the 0.01 level of signifi cance, test appropriate hypotheses to determine whether the new drug is signifi cantly more effective than the older drug in reducing high blood pressure.

The University Bookstore is facing signifi cant competition from off-campus bookstores, and they are considering targeting a specifi c class in order to retain student business. The bookstore randomly sampled 150 freshmen and 175 sophomores. They found that 46 percent of the freshmen and 40 percent of the sophomores purchase all of their textbooks at the University Bookstore. At α = 0.10, is there a signifi cant difference in the proportions of freshman and sophomores who purchase entirely at the University Bookstore?

In preparation for contract-renewal negotiations, the United Manufacturing Workers surveyed its members to see whether they preferred a large increase in retirement benefi ts or a smaller increase in salary. In a group of 1,000 male members who were polled, 743 were in favor of increased retirement benefi ts. Of 500 female members surveyed, 405 favored the increase in retirement benefi ts. (a) Calculate pˆ. (b) Compute the standard error of the difference between the two proportions. (c) Test the hypothesis that equal proportions of men and women are in favor of increased retirement benefi ts. Use the 0.05 level of signifi cance

The Coffee Institute has claimed that more than 40 percent of American adults regularly have a cup of coffee with breakfast. A random sample of 450 individuals revealed that 200 of them were regular coffee drinkers at breakfast. What is the prob value for a test of hypotheses seeking to show that the Coffee Institute’s claim was correct? (Hint: Test H0 : p = 0.4, versus H1 : p > 0.4)

Approximately what is the prob value for the test in Self-Check Exercise 9-3 on page 448?

A car retailer thinks that a 40,000-mile claim for tire life b y the manufacturer is too high. She carefully records the mileage obtained from a sample of 64 such tires. The mean turns out to be 38,500 miles. The standard deviation of the life of all tires of this type has previously been calculated by the manufacturer to be 7,600 miles. Assuming that the mileage is normally distributed, determine the largest signifi cance level at which we would accept the manufacturer’s mileage claim, that is, at which we would not conclude the mileage is signifi cantly less than 40,000 miles.

The North Carolina Department of Transportation has claimed that at most, 18 percent of passenger cars exceed 70 mph on Interstate 40 between Raleigh and Durham. A random sample of 300 cars found 48 cars exceeding 70 mph. What is the prob value for a test of hypothesis seeking to show the NCDOT’s claim is correct?

Kelly’s machine shop uses a machine-controlled metal saw to cut sections of tubing used in pressure-measuring devices. The length of the sections is normally distributed with a standard deviation of 0.06″. Twenty-fi ve pieces have been cut with the machine set to cut sections 5.00″long. When these pieces were measured, their mean length was found to be 4.97″. Use prob values to determine whether the machine should be recalibrated because the mean length is signifi cantly different from 5.00″?

SAT Services advertises that 80 percent of the time, its preparatory course will increase an individual’s score on the College Board exams by at least 50 points on the combined verbal and quantitative total score. Lisle Johns, SAT’s marketing director, wants to see whether this is a reasonable claim. He has reviewed the records of 125 students who took the course and found that 94 of them did, indeed, increase their scores by at least 50 points. Use prob values to determine whether SAT’s ads should be changed because the percentage of students whose scores increase by 50 or more points is signifi cantly different from 80 percent.

Clic Pens has tested two types of point-of-purchase displays for its new erasable pen. A shelf display was placed in a random sample of 40 stores in the test market, and a fl oor display was placed in 40 other stores in the area. The mean number of pens sold per store in one month With the shelf display was 42, and the sample standard deviation was 8. With the fl oor display, the mean number of pens sold per store in the same month was 45, and the sample standard deviation was 7. At α = 0.02, was there a signifi cant difference between sales with the two types of displays?

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