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Consider random samples of size 46 drawn from population A with proportion 0.34 and random samples of size 36 drawn from population $B$ with proportion 0.28 .
Part 1 (a) Find the standard error of the distribution of differences in sample proportions, $\hat{p}_{A}-\hat{p}_{B}$
Round your answer for the standard error to three decimal places. standard error $=$ $\square$ eTextbook and Media $\square$ Save for Later Attempts: 0 of 5 used Submit Answer
Part 2

Studdy Solution
Calculate the standard error of the difference in sample proportions:
$SE_{\hat{p}_A - \hat{p}_B} = \sqrt{SE_A^2 + SE_B^2}$
Substitute the calculated standard errors:
$SE_{\hat{p}_A - \hat{p}_B} = \sqrt{0.0698^2 + 0.0748^2}$
Calculate:
$SE_{\hat{p}_A - \hat{p}_B} = \sqrt{0.00487204 + 0.00559024} = \sqrt{0.01046228} \approx 0.1023$
Round to three decimal places:
$\boxed{0.102}$
The standard error of the distribution of differences in sample proportions is:
$$\boxed{0.102}$$