Testing Claims
You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.002 \).
\[
\begin{array}{l}
H_{o}: p=0.9 \\
H_{a}: p> 0.9
\end{array}
\]
You obtain a sample of size \( n=122 \) in which there are 121 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 \( \alpha \)
This test statistic leads to a decision to...
reject the null
accept the null
Answer
\(p\)-value\( = P(Z > 3.080) \approx 0.001\)
Step 1 ：\(\hat{p} = \frac{121}{122} \)
Step 2 ：\(z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1-p_0)}{n}}} = \frac{\frac{121}{122} - 0.9}{\sqrt{\frac{0.9 (1-0.9)}{122}}} \approx 3.080\)
Step 3 ：\(p\)-value\( = P(Z > 3.080) \approx 0.001\)
