Week 7 Homework
Score: \( 15.58 / 30 \quad 18 / 30 \) answered
Question 22
Hypothesis Test for a Population Proportion
You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.01 \).
\[
\begin{array}{l}
H_{o}: p=0.13 \\
H_{a}: p< 0.13
\end{array}
\]
You obtain a sample of size \( n=641 \) in which there are 59 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.)
\[
p \text {-value }=
\]
The \( \mathrm{p} \)-value is...
less than (or equal to) \( \alpha \)
greater than \( \alpha \)
Answer
\begin{aligned} p\text{-value}=P\left(Z<-2.485\right) \approx 0.006 \end{aligned}
Step 1 ：\begin{aligned} \text{Test Statistic }= \frac{\text{Sample Proportion} - \text{Population Proportion}}{\sqrt{\frac{\text{Population Proportion}(1- \text{Population Proportion})}{n}}} = \frac{\left(\frac{59}{641}\right) - 0.13}{\sqrt{\frac{0.13(1-0.13)}{641}}} \end{aligned}
Step 2 ：\begin{aligned} \text{Test Statistic }= \frac{\frac{59}{641}-0.13}{\sqrt{\frac{0.13(1-0.13)}{641}}}= -2.485 \end{aligned}
Step 3 ：\begin{aligned} p\text{-value}=P\left(Z<-2.485\right) \approx 0.006 \end{aligned}
