Testing Hypotheses: Two Sample Tests

Two independent samples of observations were collected. For the fi rst sample of 60 elements, the mean was 86 and the standard deviation 6. The second sample of 75 elements had a mean of 82 and a standard deviation of 9. (a) Compute the estimated standard error of the difference between the two means. (b) Using α = 0.01, test whether the two samples can reasonably be considered to have come from populations with the same mean.

In 1993, the Financial Accounting Standards Board (FASB) was considering a proposal to require companies to report the potential effect of employees’ stock options on earnings per share (EPS). A random sample of 41 high-technology fi rms revealed that the new proposal would reduce EPS by an average of 13.8 percent, with a standard deviation of 18.9 percent. A random sample of 35 producers of consumer goods showed that the proposal would reduce EPS by 9.1 percent on average, with a standard deviation of 8.7 percent. On the basis of these samples, is it reasonable to conclude (at α = 0.10) that the FASB proposal will cause a greater reduction in EPS for high-technology fi rms than for producers of consumer goods?

Two independent samples were collec ted. For the fi rst sample of 42 items, the mean was 32.3 and the variance 9. The second sample of 57 items had a mean of 34 and a variance of 16. (a) Compute the estimated standard error of the difference between the two means. (b) Using α = 0.05, test whether there is suffi cient evidence to show the second population has a larger mean.

Block Enterprises, a manufacturer of chip s for computers, is in the process of deciding whether to replace its current semiautomated assembly line with a fully automated assembly line. Block has gathered some preliminary test data about hourly chip production, which is summarized in the following table, and it would like to know whether it should upgrade its assembly line. State (and test at α = 0.02) appropriate hypotheses to help Block decide.

Two research laboratories have independently produced drugs that provide relief to arthritis sufferers. The fi rst drug was tested on a group of 90 arthritis sufferers and produced an average of 8.5 hours of relief, and a sample standard deviation of 1.8 hours. The second drug was tested on 80 arthritis sufferers, producing an average of 7.9 hours of relief, and a sample standard deviation of 2.1 hours. At the 0.05 level of signifi cance, does the second drug provide a signifi cantly shorter period of relief?

A sample of 32 money-market mutual funds was chosen on January 1, 1996, and the average annual rate of return over the past 30 days was found to be 3.23 percent, and the sample Standard deviation was 0.51 percent. A year earlier, a sample of 38 money-market funds showed an average rate of return of 4.36 percent, and the sample standard deviation was 0.84 percent. Is it reasonable to conclude (at α = 0.05) that money-market interest rates declined during 1995?

In September 1995, the Automobile Confederation of the Carolinas surveyed 75 randomly chosen service stations in North and South Carolina and determined that the average price for regular unleaded gasoline at self-service pumps was $1.059, and the sample standard deviation was 3.9¢. Three months later, another survey of 50 service stations found an average price of $1.089, and the sample standard deviation was 6.8¢. At α = 0.02, had the Carolinas’ average price of self-service regular unleaded gasoline changed signifi cantly in this 3-month period?

Notwithstanding the Equal Pay Act of 1963, in 1993 it still appeared that men earned more than women in similar jobs. A random sample of 38 male machine-tool operators found a mean hourly wage of $11.38, and the sample standard deviation was $1.84. A random sample of 45 female machine-tool operators found their mean wage to be $8.42, and the sample standard deviation was $1.31. On the basis of these samples, is it reasonable to conclude (at α = 0.01) that the male operators are earning over $2.00 more per hour than the female operators?

BullsEye Discount store has always prided itself on customer service. The store hopes that all BullsEye stores are providing the same level of service from coast to coast, so they have surveyed some customers. In the Southeast region, a random sample of 97 customers yielded an average overall satisfaction rating of 8.8 out of 10 and the sample standard deviation was 0.7. In the Northeast region, a random sample of 84 customers resulted in an average rating of 9.0 and the sample standard deviation was 0.6. Can BullsEye conclude, at α = 0.05, that the levels of customer satisfaction in the two markets are signifi cantly different?

consumer-research organization routinely selects several car models each year and evaluates their fuel effi ciency. In this year’s study of two similar subcompact models from two different automakers, the average gas mileage for 12 cars of brand A was 27.2 miles per gallon, and the standard deviation was 3.8 mpg. The nine brand B cars that were tested averaged 32.4 mpg, and the standard deviation was 4.3 mpg. At α = 0.01, should it conclude that brand A cars have lower average gas mileage than do brand B cars?

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