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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 \( =-1.826 \quad \checkmark \sigma^{\varsigma} \)
What is the \( p \)-value for this sample? (Report answer accurate to three decimal places.)
\[
p \text {-value }=0.2409 \quad x
\]
The \( \mathrm{p} \)-value is...
less than (or equal to) \( \alpha \)
greater than \( \alpha \)
Answer
3. Calculate \(p\)-value: \(p\text{\(-\)value}=2\cdot P(Z>|-1.826|)=2\cdot P(Z>1.826)=0.0676\)
Step 1 ：1. Calculate \(\hat{p}\): \(\hat{p}=\frac{106}{440}=0.2409\)
Step 2 ：2. Calculate test statistic: \(z=\frac{\hat{p}-p_{0}}{\sqrt{\frac{p_{0}(1-p_{0})}{n}}}=\frac{0.2409-0.28}{\sqrt{\frac{0.28(1-0.28)}{440}}}=-1.826\)
Step 3 ：3. Calculate \(p\)-value: \(p\text{\(-\)value}=2\cdot P(Z>|-1.826|)=2\cdot P(Z>1.826)=0.0676\)
