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Question 10
Hypothesis Test for the Difference in Two Proportions
You wish to test the following claim $(H_{a})$ at a significance level of $α = 0.005$ .
$\begin{array}{l} H_{o} : p_{1} = p_{2} \\ H_{a} : p_{1} < p_{2} \end{array}$
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 $p$ -value is...
less than (or equal to) $α$
greater than $α$
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Answer

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Answer

$p -value = 3.292 \times 10^{- 6}$

Steps

Step 1 ： $p_{1} = \frac{119}{263}$

Step 2 ： $p_{2} = \frac{182}{338}$

Step 3 ： $Test statistic = \frac{(p_{1} - p_{2})}{\sqrt{\frac{(p_{1} (1 - p_{1}))}{n_{1}} + \frac{(p_{2} (1 - p_{2}))}{n_{2}}}} = - 4.507$

Step 4 ： $p -value = 3.292 \times 10^{- 6}$