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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Testing Claims About Proportions. In Exercises 7โ22, 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 โAssociation Between Helicopter vs Ground Emergency Medical Services and Survival for Adults With Major Trauma,โ 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?
Degrees of Freedom
For Example 1 on page 431, we used df smaller of and , we got , and the corresponding critical values are If we calculate df using Formula 9-1, we get, and the corresponding critical values are . How is using the critical values of more โconservativeโ than using the critical values of .
In Exercises 5โ20, 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 โTableโ answers based on Table A-3 with df equal to the smaller of\({n_1} - 1\)and\({n_2} - 1\).)Blanking Out on Tests Many students have had the unpleasant experience of panicking on a test because the first question was exceptionally difficult. The arrangement of test items was studied for its effect on anxiety. The following scores are measures of โdebilitating test anxiety,โ which most of us call panic or blanking out (based on data from โItem Arrangement, Cognitive Entry Characteristics, Sex and Test Anxiety as Predictors of Achievement in Examination Performance,โ by Klimko, Journal of Experimental Education, Vol. 52, No. 4.) Is there sufficient evidence to support the claim that the two populations of scores have different means? Is there sufficient evidence to support the claim that the arrangement of the test items has an effect on the score? Is the conclusion affected by whether the significance level is 0.05 or 0.01?
Questions Arranged from Easy to Difficult | ||||
24.64 | 39.29 | 16.32 | 32.83 | 28.02 |
33.31 | 20.60 | 21.13 | 26.69 | 28.9 |
26.43 | 24.23 | 7.10 | 32.86 | 21.06 |
28.89 | 28.71 | 31.73 | 30.02 | 21.96 |
25.49 | 38.81 | 27.85 | 30.29 | 30.72 |
Questions Arranged from Difficult to Easy | |||
33.62 | 34.02 | 26.63 | 30.26 |
35.91 | 26.68 | 29.49 | 35.32 |
27.24 | 32.34 | 29.34 | 33.53 |
27.62 | 42.91 | 30.20 | 32.54 |
Confidence Interval for Haemoglobin
Large samples of women and men are obtained, and the haemoglobin level is measured in each subject. Here is the 95% confidence interval for the difference between the two population means, where the measures from women correspond to population 1 and the measures from men correspond to population 2: .
a. What does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in men?
b. Write a brief statement that interprets that confidence interval.
c. Express the confidence interval with measures from men being population 1 and measures from women being population 2.
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