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Chapter 9: Q1BSC (page 414)

Independent and Dependent Samples Which of the following involve independent samples?

a. Data Set 14 鈥淥scar Winner Age鈥� in Appendix B includes pairs of ages of actresses and actors at the times that they won Oscars for Best Actress and Best Actor categories. The pair of ages of the winners is listed for each year, and each pair consists of ages matched according to the year that the Oscars were won.

b. Data Set 15 鈥淧residents鈥� in Appendix B includes heights of elected presidents along with the heights of their main opponents. The pair of heights is listed for each election.

c. Data Set 26 鈥淐ola Weights and Volumes鈥� in Appendix B includes the volumes of the contents in 36 cans of regular Coke and the volumes of the contents in 36 cans of regular Pepsi.

Short Answer

Expert verified

a. It is a dependent sample.

b. It is a dependent sample.

c. It is an independent sample.

Step by step solution

01

Define independent and dependent samples

Independent samples were taken from two populations. The values are not associated with one other.

Dependent samples have a relationship between values such that each value of one sample is related to another value of another sample.

02

Identify the samples

a. Any pair of actors and actress is related by the year in which they won the Oscars. Hence, each pair consists of ages matched according to the year or time. Thus, the samples are dependent.

b. Any pair of presidents and opponents recorded for height are related by the year of election. Thus, the samples are dependent.

c. The two samples for contents of 36 cans in each group, Pepsi and Cokeare not related to each other. Thus, the samplesare independent.

Only part (c) describes independent samples.

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Most popular questions from this chapter

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 鈥淭able鈥� answers based on Table A-3 with df equal to the smaller of and)

Regular Coke and Diet Coke Data Set 26 鈥淐ola Weights and Volumes鈥� in Appendix B includes weights (lb) of the contents of cans of Diet Coke (n= 36, x炉= 0.78479 lb, s= 0.00439 lb) and of the contents of cans of regular Coke (n= 36, x炉= 0.81682 lb, s= 0.00751 lb).

a. Use a 0.05 significance level to test the claim that the contents of cans of Diet Coke have weights with a mean that is less than the mean for regular Coke.

b. Construct the confidence interval appropriate for the hypothesis test in part (a).

c. Can you explain why cans of Diet Coke would weigh less than cans of regular Coke?

Confidence Interval for Haemoglobin

Large samples of women and men are obtained, and the haemoglobin level is measured in each subject. Here is the 95% confidence interval for the difference between the two population means, where the measures from women correspond to population 1 and the measures from men correspond to population 2:\(\)\( - 1.76g/dL < {\mu _1} - {\mu _2} < - 1.62g/dL\).

a. What does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in men?

b. Write a brief statement that interprets that confidence interval.

c. Express the confidence interval with measures from men being population 1 and measures from women being population 2.

Equivalence of Hypothesis Test and Confidence Interval Two different simple random samples are drawn from two different populations. The first sample consists of 20 people with 10 having a common attribute. The second sample consists of 2000 people with 1404 of them having the same common attribute. Compare the results from a hypothesis test of p1=p2(with a 0.05 significance level) and a 95% confidence interval estimate ofp1-p2.

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.

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?

Are Flights Cheaper When Scheduled Earlier? Listed below are the costs (in dollars) of flights from New York (JFK) to Los Angeles (LAX). Use a 0.01 significance level to test the claim that flights scheduled one day in advance cost more than flights scheduled 30 days in advance. What strategy appears to be effective in saving money when flying?

Delta

Jet Blue

American

Virgin

Alaska

United

1 day in advance

501

634

633

646

633

642

30 days in advance

148

149

156

156

252

313
See all solutions

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