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AP Statistics/Unit 5: Sampling Distributions
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Standard Deviation Of Difference In Sample Proportions

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To compare the proportion of adults who exercise regularly in two cities, a researcher selected independent random samples. The sample from City A consisted of 400 adults, of whom 45% exercise regularly. The sample from City B consisted of 600 adults, of whom 38% exercise regularly. What is the standard deviation of the sampling distribution for the difference in sample proportions ($\hat{p}_A - \hat{p}_B$)?

A

0.0011

B

0.0318

C

0.0324²

D

0.45⋅0.55/400+0.38⋅0.62/600\sqrt{0.45 \cdot 0.55/400 + 0.38 \cdot 0.62/600}

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