Problem
Score: \( 16.18 / 30 \quad 20 / 30 \) answered Question 24 Testing Claims You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.002 \). \[ \begin{array}{l} H_{o}: p=0.66 \\ H_{a}: p<0.66 \end{array} \] You obtain a sample of size \( n=609 \) in which there are 393 successful observations. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic \( = \) What is the p-value for this sample? (Report answer accurate to three decimal places.) \( p \)-value \( = \) The p-value is... less than (or equal to) \( \alpha \) greater than \( \alpha \)
Solution
Step 1 ：\(Z = \frac{(p - \hat{p})}{\sqrt{\frac{p(1-p)}{n}}}\)
Step 2 ：\(Z = \frac{(0.66 - \frac{393}{609})}{\sqrt{\frac{0.66(1-0.66)}{609}}}\)
Step 3 ：\(Z = -1.810\)
Step 4 ：P(Z \le -1.810) = 0.035\)
