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ふUIC. JU.LI44 \( 1 J 14 \) aIIJVEICU
Question 10
Hypothesis Test for the Difference in Two Proportions
You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.005 \).
\[
\begin{array}{l}
H_{o}: p_{1}=p_{2} \\
H_{a}: p_{1}< p_{2}
\end{array}
\]
You obtain 119 successes in a sample of size \( n_{1}=263 \) from the first population. You obtain 182 succe in a sample of size \( n_{2}=338 \) from the second population.
What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic \( =0.65 \)
What is the p-value for this sample? (Report answer accurate to four decimal places.) \( p \)-value \( = \)
The \( \mathrm{p} \)-value is...
less than (or equal to) \( \alpha \)
greater than \( \alpha \)
Type here to search
Answer
\( p\text{-value} = 3.292 \times 10^{-6} \)
Step 1 ：\( p_1 = \frac{119}{263} \)
Step 2 ：\( p_2 = \frac{182}{338} \)
Step 3 ：\( \mathrm{Test\,statistic} = \frac{(p_1 - p_2)}{\sqrt{\frac{(p_1(1-p_1))}{n_1} + \frac{(p_2(1-p_2))}{n_2}}} = -4.507 \)
Step 4 ：\( p\text{-value} = 3.292 \times 10^{-6} \)
