# For each claim, assume the distribution of the population is approx...

## Question

For each claim, assume the distribution of the population is approximately normal.

Microwave Repair Costs ?
A microwave oven repairer says that the mean repair cost for damaged microwave ovens is less than \$100. You work for the repairer and want to test this claim. You find that a random sample of five microwave ovens has a mean repair cost of \$75 and a standard deviation of \$12.50. At a = 0.01, do you have enough evidence to support the repairer's claim?(Adapted from Consumer Reports)

Deciding on a Distribution ?
In the following two exercises, decide whether you should use a normal sampling distribution or a t-sampling distribution to perform the hypothesis test. Justify your decision. Then use the distribution to test the claim. Write a short paragraph about the results of the test and what you can conclude about the claim.

Gas Mileage ?
A car company says that the mean gas mileage for its luxury sedan is at least 21 miles per gallon (mpg). You believe the claim is incorrect and find that a random sample of 5 cars has a mean gas mileage of 19 mpg and a standard deviation of 4 mpg. Assume the gas mileage of all of the company's luxury sedans is normally distributed. At a = 0.05, test the company's claim. (Adapted from Consumer Reports)

Testing Claims ?
(a) write the claim mathematically and identify H 0 and Ha , (b) find the critical values and identify the rejection regions, (c) find the standardized test statistic, and (d) decide whether to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim.

Do You Eat Breakfast?
A medical researcher estimates that no more than 55% of U.S. adults eat breakfast every day. In a random sample of 250 U.S. adults, 56.4% say that they eat breakfast every day. At a = 0.01, is there enough evidence to reject the researcher's claim? (Adapted from U.S. National Center for Health Statistics)

Just Say No to GMO ?
An environmentalist claims that more than 50% of British consumers want supermarkets to stop selling genetically modified foods. You want to test this claim. You find that in a random sample of 100 British consumers, 53% say that they want supermarkets to stop selling genetically modified foods. At a = 0.10, can you support the environmentalist's claim?(Adapted from Friends of the Earth)
Testing Claims In Exercises 17–26, (a) write the claim mathematically and identify H 0 and Ha , (b) find the critical value(s) and identify the rejection region(s), (c) use the ?2-test to find the standardized test statistic, and (d) decide whether to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim. Assume the populations are normally distributed.

Life of Appliances ?
A large appliance company estimates that the variance of the life of its appliances is 3. You work for a consumer advocacy group and are asked to test this claim. You find that a random sample of the lives of 27 of the company's appliances has a variance of 2.8. At a = 0.05, do you have enough evidence to reject the company's claim? (Adapted from Consumer Reports)

Salaries ?
An employment information service says that the standard deviation of the annual salaries for public relations managers is at least \$14,500. The annual salaries for 18 randomly chosen public relations managers are listed. At a = 0.10, can you reject the claim? (Adapted from America's Career InfoNet)
37,517 50,217 29,177 51,744 69,422 60,770
50,549 50,263 62,939 62,372 65,014 49,164
34,811 55,413 51,310 80,433 34,185 31,805

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