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Chapter 9: Q3BSC (page 414)
Units of MeasureIf the values listed in Exercise 2 are changed so that they are expressed in Celsius degrees instead of Fahrenheit degrees, how are hypothesis test results affected?
Hypothesis test results are not affected by a change in the unit of measurement.
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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.
Dreaming in Black and White A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 306 people over the age of 55, 68 dream in black and white, and among 298 people under the age of 25, 13 dream in black and white (based on data from 鈥淒o We Dream in Color?鈥� by Eva Murzyn, Consciousness and Cognition, Vol. 17, No. 4). We want to use a 0.01 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion of those under 25.
a. Test the claim using a hypothesis test.
b. Test the claim by constructing an appropriate confidence interval.
c. An explanation given for the results is that those over the age of 55 grew up exposed to media that was mostly displayed in black and white. Can the results from parts (a) and (b) be used to verify that explanation?
In Exercises 5鈥�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 鈥淭able鈥� 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 鈥淢orbidity Among Pediatric Motor Vehicle Crash Victims: The Effectiveness of Seat Belts,鈥� 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?
In Exercises 5鈥�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 鈥淭able鈥� answers based on Table A-3 with df equal to the smaller of\({n_1} - 1\)and\({n_2} - 1\).)
Are Male Professors and Female Professors Rated Differently?
a. Use a 0.05 significance level to test the claim that two samples of course evaluation scores are from populations with the same mean. Use these summary statistics: Female professors:
n = 40, \(\bar x\)= 3.79, s = 0.51; male professors: n = 53, \(\bar x\) = 4.01, s = 0.53. (Using the raw data in Data Set 17 鈥淐ourse Evaluations鈥� will yield different results.)
b. Using the summary statistics given in part (a), construct a 95% confidence interval estimate of the difference between the mean course evaluations score for female professors and male professors.
c. Example 1 used similar sample data with samples of size 12 and 15, and Example 1 led to the conclusion that there is not sufficient evidence to warrant rejection of the null hypothesis.
Do the larger samples in this exercise affect the results much?
Robust What does it mean when we say that the F test described in this section is not robust against departures from normality?
In Exercises 5鈥�16, test the given claim.
Professor Evaluation Scores Listed below are student evaluation scores of female professorsand male professors from Data Set 17 鈥淐ourse Evaluations鈥� in Appendix B. Use a 0.05 significance level to test the claim that female professors and male professors have evaluation scores with the same variation.
Female | 4.4 | 3.4 | 4.8 | 2.9 | 4.4 | 4.9 | 3.5 | 3.7 | 3.4 | 4.8 |
Male | 4 | 3.6 | 4.1 | 4.1 | 3.5 | 4.6 | 4 | 4.3 | 4.5 | 4.3 |
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