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Chapter 9: Q1BSC (page 414)

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

a. Data Set 14 “Oscar Winner Age” 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 “Presidents” 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 “Cola Weights and Volumes” 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

Magnet Treatment of Pain People spend around $5 billion annually for the purchase of magnets used to treat a wide variety of pains. Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results given below are among the results obtained in the study (based on data from “Bipolar Permanent Magnets for the Treatment of Chronic Lower Back Pain: A Pilot Study,” by Collacott, Zimmerman, White, and Rindone, Journal of the American Medical Association, Vol. 283, No. 10). Higher scores correspond to greater pain levels.

a. Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment (similar to a placebo).

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

c. Does it appear that magnets are effective in treating back pain? Is it valid to argue that magnets might appear to be effective if the sample sizes are larger?

Reduction in Pain Level after Magnet Treatment: n = 20, x = 0.49, s = 0.96

Reduction in Pain Level after Sham Treatment: n = 20, x = 0.44, s = 1.4

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.

Clinical Trials of OxyContin OxyContin (oxycodone) is a drug used to treat pain, butit is well known for its addictiveness and danger. In a clinical trial, among subjects treatedwith OxyContin, 52 developed nausea and 175 did not develop nausea. Among other subjectsgiven placebos, 5 developed nausea and 40 did not develop nausea (based on data from PurduePharma L.P.). Use a 0.05 significance level to test for a difference between the rates of nauseafor those treated with OxyContin and those given a placebo.

a. Use a hypothesis test.

b. Use an appropriate confidence interval.

c. Does nausea appear to be an adverse reaction resulting from OxyContin?

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.

Lefties In a random sample of males, it was found that 23 write with their left hands and 217 do not. In a random sample of females, it was found that 65 write with their left hands and 455 do not (based on data from “The Left-Handed: Their Sinister History,” by ElaineFowler Costas, Education Resources Information Center, Paper 399519). We want to use a 0.01significance level to test the claim that the rate of left-handedness among males is less than that among females.

a. Test the claim using a hypothesis test.

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

c. Based on the results, is the rate of left-handedness among males less than the rate of left-handedness among females?

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?

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\({n_2} - 1\).) Bad Stuff in Children’s Movies Data Set 11 “Alcohol and Tobacco in Movies” in Appendix B includes lengths of times (seconds) of tobacco use shown in animated children’s movies. For the Disney movies, n = 33,\(\bar x\)= 61.6 sec, s = 118.8 sec. For the other movies, n = 17,\(\bar x\)= 49.3 sec, s = 69.3 sec. The sorted times for the non-Disney movies are listed below.

a. Use a 0.05 significance level to test the claim that Disney animated children’s movies and other animated children’s movies have the same mean time showing tobacco use.

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

c. Conduct a quick visual inspection of the listed times for the non-Disney movies and comment on the normality requirement. How does the normality of the 17 non-Disney times affect the results?

0 0 0 0 0 0 1 5 6 17 24 55 91 117 155 162 205
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