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.
Overlap of Confidence Intervals In the article “On Judging the Significance of Differences by Examining the Overlap Between Confidence Intervals,” by Schenker and Gentleman (American Statistician, Vol. 55, No. 3), the authors consider sample data in this statement: “Independent 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.”
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 \({p_2}\)?
