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Chapter 9: Q4BSC (page 414)

Robust What does it mean when we say that the F test described in this section is not robust against departures from normality?

Short Answer

Expert verified

The given statement means that the F test will not give the desired and accurate results if the populations from which the samples are extracted are not normally distributed, irrespective of the sample size.

Step by step solution

01

Given information

It is given that the F test is not robust against departures from normality.

02

Interpretation of the F-test not being robust

In statistics, robust means that a statistic works well for the given hypothesis test and produces a correct conclusion.

If the distribution of the test statistic is robust against departure from normality, it implies that the distribution is not very strict about the requirement of the population to be normally distributed and will produce accurate results even if the population is not normally distributed.

If the distribution of the test statistic is not robust against departure from normality, the distribution is very strict about the requirement of the population to be normally distributed and will not work well if the population is not normally distributed.

Therefore, the F test is not robust against departure from normality and will not give accurate results if the populations from which the samples are extracted are not normally distributed, irrespective of the sample size.

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Most popular questions from this chapter

Does Aspirin Prevent Heart Disease? In a trial designed to test the effectiveness of aspirin in preventing heart disease, 11,037 male physicians were treated with aspirin and 11,034 male physicians were given placebos. Among the subjects in the aspirin treatment group, 139 experienced myocardial infarctions (heart attacks). Among the subjects given placebos, 239 experienced myocardial infarctions (based on data from 鈥淔inal Report on the Aspirin Component of the Ongoing Physicians鈥� Health Study,鈥� New England Journal of Medicine, Vol. 321: 129鈥�135). Use a 0.05 significance level to test the claim that aspirin has no effect on myocardial infarctions.

a. Test the claim using a hypothesis test.

b. Test the claim by constructing an appropriate confidence interval.

c. Based on the results, does aspirin appear to be effective?

Using Confidence Intervals

a. Assume that we want to use a 0.05 significance level to test the claim that p1 < p2. Which is better: A hypothesis test or a confidence interval?

b. In general, when dealing with inferences for two population proportions, which two of the following are equivalent: confidence interval method; P-value method; critical value method?

c. If we want to use a 0.05 significance level to test the claim that p1 < p2, what confidence level should we use?

d. If we test the claim in part (c) using the sample data in Exercise 1, we get this confidence interval: -0.000508 < p1 - p2 < - 0.000309. What does this confidence interval suggest about the claim?

Hypothesis Tests and Confidence Intervals for Hemoglobin

a. Exercise 2 includes a confidence interval. If you use the P-value method or the critical value method from Part 1 of this section to test the claim that women and men have the same mean hemoglobin levels, will the hypothesis tests and the confidence interval result in the same conclusion?

b. In general, if you conduct a hypothesis test using the methods of Part 1 of this section, will the P-value method, the critical value method, and the confidence interval method result in the same conclusion?

c. Assume that you want to use a 0.01 significance level to test the claim that the mean haemoglobin level in women is lessthan the mean hemoglobin level in men. What confidence level should be used if you want to test that claim using a confidence interval?

In Exercises 5鈥�16, use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal.

Heights of Mothers and Daughters Listed below are heights (in.) of mothers and their first daughters. The data are from a journal kept by Francis Galton. (See Data Set 5 鈥淔amilyHeights鈥� in Appendix B.) Use a 0.05 significance level to test the claim that there is no difference in heights between mothers and their first daughters.

Height of Mother

68

60

61

63.5

69

64

69

64

63.5

66

Height of Daughter

68.5

60

63.5

67.5

68

65.5

69

68

64.5

63

Testing Claims About Proportions. In Exercises 7鈥�22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.

Are Seat Belts Effective? A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2823 occupants not wearing seat belts, 31 were killed. Among 7765 occupants wearing seat belts, 16 were killed (based on data from 鈥淲ho Wants Airbags?鈥� by Meyer and Finney, Chance, Vol. 18, No. 2). We want to use a 0.05 significance level to test the claim that seat belts are effective in reducing fatalities.

a. Test the claim using a hypothesis test.

b. Test the claim by constructing an appropriate confidence interval.

c. What does the result suggest about the effectiveness of seat belts?
See all solutions

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