Cola Weights Data Set 37 “Cola Weights and Volumes” in Appendix B lists the weights (lb) of the contents of cans of cola from four different samples: (1) regular Coke, (2) Diet Coke, (3) regular Pepsi, and (4) Diet Pepsi. The results from analysis of variance are shown in the Minitab display below. What is the null hypothesis for this analysis of variance test? Based on the displayed results, what should you conclude about H_knot. What do you conclude about equality of the mean weights from the four samples?
9. Hypothesis Testing for One Sample
Steps in Hypothesis Testing
- Textbook Question
- Textbook Question
Cola Weights For the four samples described in Exercise 1, the sample of regular Coke has a mean weight of 0.81682 lb, the sample of Diet Coke has a mean weight of 0.78479 lb, the sample of regular Pepsi has a mean weight of 0.82410 lb, and the sample of Diet Pepsi has a mean weight of 0.78386 lb. If we use analysis of variance and reach a conclusion to reject equality of the four sample means, can we then conclude that any of the specific samples have means that are significantly different from the others?
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Cola Weights The displayed results from Exercise 1 are from one-way analysis of variance. What is it about this test that characterizes it as one-way analysis of variance instead of two-way analysis of variance?
- Textbook Question
In Exercises 9–12, use the sign test for the claim involving nominal data.
Medical Malpractice In a study of 1228 randomly selected medical malpractice lawsuits, it was found that 856 of them were dropped or dismissed (based on data from the Physicians Insurers Association of America). Use a 0.01 significance level to test the claim that there is a difference between the rate of medical malpractice lawsuits that go to trial and the rate of such lawsuits that are dropped or dismissed.
- Textbook Question
In Exercises 9–12, use the sign test for the claim involving nominal data.
Overtime Rule in Football Before the overtime rule in the National Football League was changed in 2011, among 460 overtime games, 252 were won by the team that won the coin toss at the beginning of overtime. Using a 0.05 significance level, test the claim that the coin toss is fair in the sense that neither team has an advantage by winning it. Does the coin toss appear to be fair?
- Textbook Question
In Exercises 13–16, refer to the indicated data set in Appendix B and use the sign test for the claim about the median of a population.
Cotinine in Smokers Data Set 15 “Passive and Active Smoke” includes cotinine measurements from 902 smokers. Cotinine is a biomarker of nicotine in the body. Use a 0.01 significance level to test the claim that smokers have cotinine levels with a median of 2.84 ng/mL, which is the median for nonsmokers not exposed to tobacco smoke.
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Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:
a. Differences d
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Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:
b. The ranks corresponding to the nonzero values of |d|
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Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:
c. The signed ranks
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Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:
d. The sum of the positive ranks and the sum of the absolute values of the negative ranks
- Textbook Question
Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:
f. The critical value of T (assuming a 0.05 significance level in a test of no difference between hospital admissions of Friday 6th and the following Friday 13th).
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Correlation and Slope What is the relationship between the linear correlation coefficient r and the slope b1 of a regression line?
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Appendix B Data Sets
In Exercises 13–16, use the data in Appendix B to test for rank correlation with a 0.05 significance level.
Taxis Refer to Data Set 32 “Taxis” in Appendix B and use the distances (miles) and tip amounts (dollars) of all of the rides. Is there sufficient evidence to support the claim that there is a correlation between the distance of the ride and the tip amount? Does it appear that riders base their tips on the distance of the ride?
- Textbook Question
In Exercises 1–4, use the following sequence of political party affiliations of recent presidents of the United States, where R represents Republican and D represents Democrat.
Runs Test If we use a 0.05 significance level to test for randomness, what are the critical values from Table A-10? Based on those values and the number of runs from Exercise 2, what should be concluded about randomness?
- Textbook Question
In Exercises 1–4, use the following sequence of political party affiliations of recent presidents of the United States, where R represents Republican and D represents Democrat.
Good Sample? Given the sequence of data, if we fail to reject randomness, does it follow that the sampling method is suitable for statistical methods? Explain.