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 \( \alpha \)
Answer
P(Z \le -1.810) = 0.035\)
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\)
