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Hypothesis Test for a Population Proportion
You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.05 \).
\[
\begin{array}{l}
H_{o}: p=0.86 \\
H_{a}: p> 0.86
\end{array}
\]
You obtain a sample of size \( n=257 \) in which there are 233 successful observation
What is the test statistic for this sample? (Report answer accurate to three decima test statistic \( = \)
What is the \( p \)-value for this sample? (Report answer accurate to three decimal place \( p \)-value \( = \)
The \( \mathrm{p} \)-value is...
less than (or equal to) \( \alpha \)
greater than \( \alpha \)
\( 6^{6} \)
This test statistic leads to a decision to...
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Answer
\( p \)-value \( \approx 0.002 \)
Step 1 ：\( Z = \frac{(\frac{233}{257}) - 0.86}{\sqrt{\frac{0.86(1-0.86)}{257}}} \)
Step 2 ：\( Z \approx 2.921 \)
Step 3 ：\( p \)-value \( \approx 0.002 \)
