# Hypothesis Testing: Mean, Variance & Proportion

Problems 23 & 37

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

23. 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?

Deciding on a Distribution 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.

37. 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.

Problems 11 & 13

Testing Claims (a) write the claim mathematically and identify and (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.

11. Environmentally Conscious Consumers ◆ You are employed by an environmental conservation agency that recently claimed more than 30% of U.S. consumers have stopped buying a certain product because the manufacturing of the product pollutes the environment. You want to test this claim.To do so, you randomly select 1050 U.S. consumers and find that 32% have stopped buying this product because of pollution concerns. At a = 0.03, can you support the claim?

13. Government Regulations Harmful? ◆ In your work for a business regulatory agency, you find that in a sample of 1762 people in the U.S., 1004 of them believe that government regulation of business does more harm than good. At a = 0.02, can you reject the claim that 60% of people in the U.S. have this view?

Problems 17 & 25

Testing Claims (a) write the claim mathematically and identify and (b) find the critical value(s) and identify the rejection region(s), (c) use the 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.

17. 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?

25. Salaries ◆ The annual salaries of 16 randomly chosen actuaries are listed below. At a = 0.05, can you conclude that the standard deviation of the annual salaries is greater than $20,000?

45,018 34,952 85,517 45,553 41,900 76,384 48,862 37,615

61,104 96,710 97,875 68,245 39,945 53,582 65,252 72,522

https://brainmass.com/statistics/hypothesis-testing/hypothesis-testing-mean-variance-proportion-324717

#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.