# Chapter 1. The Sampling Distribution of a Difference Between Proportions

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Stat Tutor
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### Question 1.1

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Incorrect. p1 - p2 is the mean of the sampling distribution of $$\widehat{p}_{1}$$ - $$\widehat{p}_{2}$$.
Correct. p1 - p2 is the mean of the sampling distribution of $$\widehat{p}_{1}$$ - $$\widehat{p}_{2}$$.
Incorrect. Try again.
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### Question 1.2

Incorrect. $$\sqrt{ \frac{ p_{1}(1- p_{1})}{ n_{1} } + \frac{p_{2}(1- p_{2})}{ n_{2} } }$$ is the standard deviation of the sampling distribution of $$\widehat{p}_{1}$$ - $$\widehat{p}_{2}$$.
Correct. $$\sqrt{ \frac{ p_{1}(1- p_{1})}{ n_{1} } + \frac{p_{2}(1- p_{2})}{ n_{2} } }$$ is the standard deviation of the sampling distribution of $$\widehat{p}_{1}$$ - $$\widehat{p}_{2}$$.
Incorrect. The shape of the sampling distribution of $$\widehat{p}_{1}$$ - $$\widehat{p}_{2}$$ is approximately Normal provided n1p1 $$\geq$$ 5, n1(1-p1) $$\geq$$ 5, n2p2 $$\geq$$ 5, and n2(1-p2) $$\geq$$ 5.
Correct. The shape of the sampling distribution of $$\widehat{p}_{1}$$ - $$\widehat{p}_{2}$$ is approximately Normal provided n1p1 $$\geq$$ 5, n1(1-p1) $$\geq$$ 5, n2p2 $$\geq$$ 5, and n2(1-p2) $$\geq$$ 5.