Question 23
Testing Claims
You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.002 \).
\[
\begin{array}{l}
H_{o}: p=0.28 \\
H_{a}: p \neq 0.28
\end{array}
\]
You obtain a sample of size \( n=440 \) in which there are 106 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 \( \mathrm{p} \)-value is...
less than (or equal to) \( \alpha \)
greater than \( \alpha \)
This test statistic leads to a decision to...
Answer
\( p \)-value \( = 2*P(Z>|z|) \)
Step 1 ：\( \hat{p} = \frac{106}{440} \)
Step 2 ：\( z = \frac{\hat{p} - p_{0}}{\sqrt{\frac{p_{0}(1-p_{0})}{n}}} = \frac{\frac{106}{440} - 0.28}{\sqrt{\frac{0.28(1-0.28)}{440}}} \)
Step 3 ：\( p \)-value \( = 2*P(Z>|z|) \)
