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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Degrees of Freedom
For Example 1 on page 431, we used df\( = \)smaller of\({n_1} - 1\)and\({n_2} - 1\), we got\(df = 11\), and the corresponding critical values are\(t = \pm 2.201.\)If we calculate df using Formula 9-1, we get\(df = 19.063\), and the corresponding critical values are\( \pm 2.093\). How is using the critical values of\(t = \pm 2.201\)more “conservative” than using the critical values of\( \pm 2.093\).
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.
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 “Do We Dream in Color?” 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?
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.
Ground vs. Helicopter for Serious Injuries A study investigated rates of fatalities among patients with serious traumatic injuries. Among 61,909 patients transported by helicopter, 7813 died. Among 161,566 patients transported by ground services, 17,775 died (based on data from “Association Between Helicopter vs Ground Emergency Medical Services and Survival for Adults With Major Trauma,” by Galvagno et al., Journal of the American Medical Association, Vol. 307, No. 15). Use a 0.01 significance level to test the claim that the rate of fatalities is higher for patients transported by helicopter.
a. Test the claim using a hypothesis test.
b. Test the claim by constructing an appropriate confidence interval.
c. Considering the test results and the actual sample rates, is one mode of transportation better than the other? Are there other important factors to consider?
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
We have specified a margin of error, a confidence level, and a likely range for the observed value of the sample proportion. For each exercise, obtain a sample size that will ensure a margin of error of at most the one specified (provided of course that the observed value of the sample proportion is further from than the educated guess).Obtain a sample size that will ensure a margin of error of at most the one specified.
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