Discuss the below:
Using and Interpreting Concepts
Testing Claims In Q1 and Q2
(a) write the claim mathematically and identify Ho and Ha
(b) find the critical value(s) and identify the rejection region(s).
(c) find the standardized test statistic.
(d) decide whether to reject or fail to reject the null hypothesis.
(e) interpret the decision in the context of the original claim.
For each claim, assume the population is normally distributed.
Q1. 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 Q2 and Q3, decide whether you should use a normal sampling distribution or a 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.
Q2. 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 five 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)
Using and Interpreting Concepts
Testing Claims (a) write the claim mathematically and identify H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
Q3. 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 they eat breakfast every day. At a = 0.01is there enough evidence to reject the researcher's claim? (Adapted from U.S. National Center for Health Statistics)
Free Samples In Q4 and Q5, use the graph, which shows what adults think about the effectiveness of free samples.
Free Samples
Work
How effective adults say
free samples are:
More likely to buy a product 52%
Shouldn't do it 3%
Nice, but not necessary 25%
More likely to remember a product 20%
Q4. Do Free Samples Work? You interview a random sample of 50 adults. The results of the survey show that 48% of the adults said they were more likely to buy a product when there are free samples. At a = 0.05,can you reject the claim that at least 52% of the adults are more likely to buy a product when there are free samples?
Using and Interpreting Concepts
Testing Claims In Q5-Q6, (a) write the claim mathematically and identify H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) use the x2 test to find the standardized test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. For each claim, assume the population is normally distributed.
Q5. Physical Science Assessment Tests On a physical science assessment test, the scores of a random sample of 22 eighth grade students have a standard deviation of 27.7. This result prompts a test administrator to claim that the standard deviation for eighth graders on the examination is less than 29.At a = 0.10, is there enough evidence to support the administrator's claim? (Adapted from National Center for Educational Statistics)
Q6. 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)
47,517 60,217 39,177 61,744 79,422 70,770
60,549 60,263 72,939 72,372 75,014 59,164
44,811 65,413 61,310 90,433 44,185 41,805