Question 23
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Testing Claims
You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.001 \).
\[
\begin{array}{l}
H_{o}: p=0.8 \\
H_{a}: p< 0.8
\end{array}
\]
You obtain a sample of size \( n=186 \) in which there are 142 successful observations.
What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic \( = \)
What is the \( \mathrm{p} \)-value for this sample? (Report answer accurate to three decimal places.) \( \mathrm{p} \)-value \( = \)
The \( p \)-value is...
less than (or equal to) \( \alpha \)
Answer
Find the p-value using a standard normal distribution table or calculator
Step 1 ：Calculate the sample proportion: \(\hat{p} = \frac{142}{186}\)
Step 2 ：Compute the test statistic: \(z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}\)
Step 3 ：Find the p-value using a standard normal distribution table or calculator
