Question 10.133

For Exercises 19–22, a $100 (1 - α) %$ $Z$ confidence interval for $p_{1} - p_{2}$ is given. Use the confidence interval to test, using level of significance $α$ , whether $p_{1} - p_{2}$ differs from each of the indicated hypothesized values.

Question 10.133

21. A 90% $Z$ confidence interval for $p_{1} - p_{2}$ is (0.1, 0.11). Hypothesized values are

0.151
0.115
0.105

10.3.21

(a) $H_{0} : p_{1} - p_{2} = 0.151 vs . H_{a} : p_{1} - p_{2} \neq 0.151$ . The hypothesized value of 0.151 lies outside of the interval (0.1, 0.11), so we reject $H_{0}$ at the $α = 0.10$ level of significance. (b) $H_{0} : p_{1} - p_{2} = 0.115 vs . H_{a} : p_{1} - p_{2} \neq 0.115$ . The hypothesized value of 0.115 lies outside of the interval (0.1, 0.11), so we reject $H_{0}$ at the $α = 0.10$ level of significance. (c) $H_{0} : p_{1} - p_{2} = 0.105 vs . H_{a} : p_{1} - p_{2} \neq 0.105$ . The hypothesized value of 0.105 lies inside of the interval (0.1, 0.11), so we do not reject $H_{0}$ at the $α = 0.10$ level of significance.