Testing Hypotheses: Two Sample Tests

Connie Rodrigues, the Dean of Students at Midstate College, is wondering about grade distributions at the school. She has heard grumblings that the GPAs in the Business School are about 0.25 lower than those in the College of Arts and Sciences. A quick random sampling produced the following GPAs.

A credit-insurance organization has developed a new high-tech method of training new sales personnel. The company sampled 16 employees who were trained the original way and found average daily sales to be $688 and the sample standard deviation was $32.63. They also sampled 11 employees who were trained using the new method and found average daily sales to be $706 and the sample standard deviation was $24.84. At α = 0.05, can the company conclude that average daily sales have increased under the new plan?

A large stock-brokerage fi rm wants to determine how successful its new account executives have been at recruiting clients. After completing their training, new account execs spend several weeks calling prospective clients, trying to get the prospects to open accounts with the fi rm. The following data give the numbers of new accounts opened in their fi rst 2 weeks by 10 randomly chosen female account execs and by 8 randomly chosen male account execs. At α = 0.05, does it appear that the women are more effective at generating new accounts than the men are?

To celebrate their fi rst anniversary, Randy Nelson decided to buy a pair of diamond earrings for his wife Debbie. He was shown nine pairs with marquise gems weighing approximately 2 carats per pair. Because of differences in the colors and qualities of the stones, the prices varied from set to set. The average price was $2,990, and the sample standard deviation was $370. He also looked at six pairs with pear-shaped stones of the same 2-carat approximate weight. These earrings had an average price of $3,065, and the standard deviation was $805. On the basis of this evidence, can Randy conclude (at a signifi cance level of 0.05) that pearshaped diamonds cost more, on average, than marquise diamonds?

A sample of 30-year conventional mortgage rates at 11 randomly chosen banks in California yielded a mean rate of 7.61 percent and a standard deviation of 0.39 percent. A similar sample taken at 8 randomly chosen banks in Pennsylvania had a mean rate of 7.43 percent, and a standard deviation of 0.56 percent. Do these samples provide evidence to conclude (at α = 0.10) that conventional mortgage rates in California and Pennsylvania come from populations with different means?

Because refunds are paid more quickly on tax returns that are fi led electronically, the Commissioner of the Internal Revenue Service was wondering whether refunds due on returns fi led by mail were smaller than those due on returns fi led electronically. Looking only at returns claiming refunds, a sample of 17 fi led by mail had an average refund of $563, and a standard deviation of $378. The average refund on a sample of 13 electronically fi led returns was $958, and the sample standard deviation was $619. At α = 0.01, do these data support the commissioner’s speculation?

Greatyear tires currently produces tires at their Wilmington, North Carolina plant during two 12-hour shifts. The night-shift employees are planning to ask for a raise because they believe they are producing more tires per shift than the day shift. “Because Greatyear is making more money during the night shift, those employees should also make more money” according to the night-shift spokesman. I. M. Checking, the Greatyear production supervisor, randomly selected some daily production runs from each shift with the results given below (in 1,000s of tires produced).

Sherri Welch is a quality control engineer with the windshield wiper manufacturing division of Emsco, Inc. Emsco is currently considering two new synthetic rubbers for its wiper blades, and Sherri was charged with seeing whether blades made with the two new compounds wear equally well. She equipped 12 cars belonging to other Emsco employees with one blade made of each of the two compounds. On cars 1 to 6, the right blade was made of compound A and the left blade was made of compound B; on cars 7 to 12, compound A was used for the left blade. The cars were driven under normal operating conditions until the blades no longer did a satisfactory job of clearing the windshield of rain. The data below give the usable life (in days) of the blades. At α = 0.05, do the two compounds wear equally well?.

Nine computer-components dealers in major metropolitan areas were asked for their prices on two similar color inkjet printers. The results of this survey are given below. At α = 0.05, is it reasonable to assert that, on average, the Apson printer is less expensive than the Okay data printer?

The data below are a random sample of 9 firms chosen from the “Digest of Earnings Reports” in The Wall Street Journal on February 6,1992:

Find the mean change in earnings per share between 1991 and 1992.
Find the standard deviation of the change and the standard error of the mean.
Were average earnings per share different in 1991 and 1992? Test at α = 0.02.

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