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Chapter 9: Q3BSC (page 414)

Testing Normality For the hypothesis test describ\({n_2} = 153\)ed in Exercise 2, the sample sizes are\({n_1} = 147\)and. When using the Ftest with these data, is it correct to reason that there is no need to check for normality because \({n_1} > 30\)and\({n_2} > 30\)?

Short Answer

Expert verified

Although the samples have more than 30 values, the Ftestrequires that the samples must be strictly normally distributed regardless of how large the samples are.

Thus, the given reason is incorrect.

Step by step solution

01

Given information

A sample of size 147 is considered showing the heights of women. Another sample of size 153 is considered showing the heights of men.

02

Normality requirement of F test

To perform the F test, it is a strict requirement that the populations from which the two samples are taken should be normally distributed, irrespective of their sample sizes.

Here, it is mentioned that the sample sizes of the two samples are large (147 and 153). Hence, there is no need to check for the normality of the populations.

This reason is incorrect because the F test will not result in an accurate conclusion if the samples are not from normally distributed populations.

Thus, it is important to check the normality using normal quantile plots. One cannot rely on the samples being large in order to perform the F test.

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Most popular questions from this chapter

Testing Claims About Proportions. In Exercises 7–22, 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.

Overlap of Confidence Intervals In the article “On Judging the Significance of Differences by Examining the Overlap Between Confidence Intervals,” by Schenker and Gentleman (American Statistician, Vol. 55, No. 3), the authors consider sample data in this statement: “Independent simple random samples, each of size 200, have been drawn, and 112 people in the first sample have the attribute, whereas 88 people in the second sample have the attribute.”

a. Use the methods of this section to construct a 95% confidence interval estimate of the difference p1-p2. What does the result suggest about the equality of p1andp2?

b. Use the methods of Section 7-1 to construct individual 95% confidence interval estimates for each of the two population proportions. After comparing the overlap between the two confidence intervals, what do you conclude about the equality ofp1andp2?

c. Use a 0.05 significance level to test the claim that the two population proportions are equal. What do you conclude?

d. Based on the preceding results, what should you conclude about the equality ofp1andp2? Which of the three preceding methods is least effective in testing for the equality ofp1andp2?

A sample size that will ensure a margin of error of at most the one specified.

Testing Claims About Proportions. In Exercises 7–22, 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.

Tennis Challenges Since the Hawk-Eye instant replay system for tennis was introduced at the U.S. Open in 2006, men challenged 2441 referee calls, with the result that 1027 of the calls were overturned. Women challenged 1273 referee calls, and 509 of the calls were overturned. We want to use a 0.05 significance level to test the claim that men and women have equal success in challenging calls.

a. Test the claim using a hypothesis test.

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

c. Based on the results, does it appear that men and women have equal success in challenging calls?

In Exercises 5–20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with “Table” answers based on Table A-3 with df equal to the smaller of\({n_1} - 1\)and\({n_2} - 1\).)Blanking Out on Tests Many students have had the unpleasant experience of panicking on a test because the first question was exceptionally difficult. The arrangement of test items was studied for its effect on anxiety. The following scores are measures of “debilitating test anxiety,” which most of us call panic or blanking out (based on data from “Item Arrangement, Cognitive Entry Characteristics, Sex and Test Anxiety as Predictors of Achievement in Examination Performance,” by Klimko, Journal of Experimental Education, Vol. 52, No. 4.) Is there sufficient evidence to support the claim that the two populations of scores have different means? Is there sufficient evidence to support the claim that the arrangement of the test items has an effect on the score? Is the conclusion affected by whether the significance level is 0.05 or 0.01?

Questions Arranged from Easy to Difficult

24.64

39.29

16.32

32.83

28.02

33.31

20.60

21.13

26.69

28.9

26.43

24.23

7.10

32.86

21.06

28.89

28.71

31.73

30.02

21.96

25.49

38.81

27.85

30.29

30.72

Questions Arranged from Difficult to Easy

33.62

34.02

26.63

30.26

35.91

26.68

29.49

35.32

27.24

32.34

29.34

33.53

27.62

42.91

30.20

32.54

Braking Reaction Times: Boxplots Use the same data from Exercise 6 and use the same scale to construct a boxplot of the braking reaction times of males and another boxplot for the braking reaction times of females. What do the boxplots suggest?
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