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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 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.
Overlap of Confidence Intervals In the article 鈥淥n Judging the Significance of Differences by Examining the Overlap Between Confidence Intervals,鈥� by Schenker and Gentleman (American Statistician, Vol. 55, No. 3), the authors consider sample data in this statement: 鈥淚ndependent simple random samples, each of size 200, have been drawn, and 112 people in the first sample have the attribute, whereas 88 people in the second sample have the attribute.鈥�
a. Use the methods of this section to construct a 95% confidence interval estimate of the difference\({p_1} - {p_2}\). What does the result suggest about the equality of \({p_1}\) and \({p_2}\)?
b. Use the methods of Section 7-1 to construct individual 95% confidence interval estimates for each of the two population proportions. After comparing the overlap between the two confidence intervals, what do you conclude about the equality of \({p_1}\) and \({p_2}\)?
c. Use a 0.05 significance level to test the claim that the two population proportions are equal. What do you conclude?
d. Based on the preceding results, what should you conclude about the equality of \({p_1}\) and \({p_2}\)? Which of the three preceding methods is least effective in testing for the equality of \({p_1}\) and \({p_2}\)?
Repeat Exercise 12 鈥淚Q and Lead鈥� by assuming that the two population standard deviations are equal, so \({\sigma _1} = {\sigma _2}\). Use the appropriate method from Part 2 of this section. Does pooling the standard deviations yield results showing greater significance?
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.
Smoking Cessation Programs Among 198 smokers who underwent a 鈥渟ustained care鈥� program, 51 were no longer smoking after six months. Among 199 smokers who underwent a 鈥渟tandard care鈥� program, 30 were no longer smoking after six months (based on data from 鈥淪ustained Care Intervention and Postdischarge Smoking Cessation Among Hospitalized Adults,鈥� by Rigotti et al., Journal of the American Medical Association, Vol. 312, No. 7). We want to use a 0.01 significance level to test the claim that the rate of success for smoking cessation is greater with the sustained care program.
a. Test the claim using a hypothesis test.
b. Test the claim by constructing an appropriate confidence interval.
c. Does the difference between the two programs have practical significance?
Degrees of FreedomIn Exercise 20 鈥淏lanking Out on Tests,鈥� using the 鈥渟maller of\({n_1} - 1\) and \({n_2} - 1\)鈥� for the number of degrees of freedom results in df = 15. Find the number of degrees of freedom using Formula 9-1. In general, how are hypothesis tests and confidence intervals affected by using Formula 9-1 instead of the 鈥渟maller of \({n_1} - 1\)and \({n_2} - 1\)鈥�?
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.
Lefties In a random sample of males, it was found that 23 write with their left hands and 217 do not. In a random sample of females, it was found that 65 write with their left hands and 455 do not (based on data from 鈥淭he Left-Handed: Their Sinister History,鈥� by ElaineFowler Costas, Education 91影视 Information Center, Paper 399519). We want to use a 0.01significance level to test the claim that the rate of left-handedness among males is less than that among females.
a. Test the claim using a hypothesis test.
b. Test the claim by constructing an appropriate confidence interval.
c. Based on the results, is the rate of left-handedness among males less than the rate of left-handedness among females?
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