Chapter 9: Q5CRE (page 414)
Assessing Normality Interpret the normal quantile plot of heights of fathers.
The normal quartile plot showsthat there are no outliers in the observations and the graph follows an approximately normal distribution.
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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\({n_2} - 1\).) Car and Taxi Ages When the author visited Dublin, Ireland (home of Guinness Brewery employee William Gosset, who first developed the t distribution), he recorded the ages of randomly selected passenger cars and randomly selected taxis. The ages can be found from the license plates. (There is no end to the fun of traveling with the author.) The ages (in years) are listed below. We might expect that taxis would be newer, so test the claim that the mean age of cars is greater than the mean age of taxis.
Car Ages | 4 | 0 | 8 | 11 | 14 | 3 | 4 | 4 | 3 | 5 | 8 | 3 | 3 | 7 | 4 | 6 | 6 | 1 | 8 | 2 | 15 | 11 | 4 | 1 | 1 | 8 |
Taxi Ages | 8 | 8 | 0 | 3 | 8 | 4 | 3 | 3 | 6 | 11 | 7 | 7 | 6 | 9 | 5 | 10 | 8 | 4 | 3 | 4 |
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.
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\({n_2} - 1\).)
BMI We know that the mean weight of men is greater than the mean weight of women, and the mean height of men is greater than the mean height of women. A person’s body mass index (BMI) is computed by dividing weight (kg) by the square of height (m). Given below are the BMI statistics for random samples of females and males taken from Data Set 1 “Body Data” in Appendix B.
a. Use a 0.05 significance level to test the claim that females and males have the same mean BMI.
b. Construct the confidence interval that is appropriate for testing the claim in part (a).
c. Do females and males appear to have the same mean BMI?
Female BMI: n = 70, \(\bar x\) = 29.10, s = 7.39
Male BMI: n = 80, \(\bar x\) = 28.38, s = 5.37
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\({n_2} - 1\).)
Seat Belts A study of seat belt use involved children who were hospitalized after motor vehicle crashes. For a group of 123 children who were wearing seat belts, the number of days in intensive care units (ICU) has a mean of 0.83 and a standard deviation of 1.77. For a group of 290 children who were not wearing seat belts, the number of days spent in ICUs has a mean of 1.39 and a standard deviation of 3.06 (based on data from “Morbidity Among Pediatric Motor Vehicle Crash Victims: The Effectiveness of Seat Belts,” by Osberg and Di Scala, American Journal of Public Health, Vol. 82, No. 3).
a. Use a 0.05 significance level to test the claim that children wearing seat belts have a lower mean length of time in an ICU than the mean for children not wearing seat belts.
b. Construct a confidence interval appropriate for the hypothesis test in part (a).
c. What important conclusion do the results suggest?
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?
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