A simple random sample of size $$ n=1000 $$ is obtained from a population whose size is $$ \mathrm{N}=1,500,000 $$ and whose population proportion with a specified characteristic is $$ p=0.33 $$. (a) Describe the sampling distribution of $$ \hat{p} $$. Choose the phrase that best describes the shape of the sampling distribution. A. Not normal because $$ n \leq 0.05 \mathrm{~N} $$ and $$ \mathrm{np}(1-\mathrm{p})

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A simple random sample of size $$ n=1000 $$ is obtained from a population whose size is $$ \mathrm{N}=1,500,000 $$ and whose population proportion with a specified characteristic is $$ p=0.33 $$. (a) Describe the sampling distribution of $$ \hat{p} $$. Choose the phrase that best describes the shape of the sampling distribution. A. Not normal because $$ n \leq 0.05 \mathrm{~N} $$ and $$ \mathrm{np}(1-\mathrm{p})<10 $$ C. Approximately normal because $$ \mathrm{n} \leq 0.05 \mathrm{~N} $$ and $$ \mathrm{np}(1-\mathrm{p}) \geq 10 $$ D. Approximately normal because $$ \mathrm{n} \leq 0.05 \mathrm{~N} $$ and $$ \mathrm{np}(1-\mathrm{p})<10 $$ Determine the mean of the sampling distribution of $$ \hat{\mathrm{p}} $$. $$ \mu_{\hat{p}}=\square $$ (Round to two decimal places as needed.)

Schultz Chen · Accepted Answer

The sampling distribution of $$ \hat{p} $$ is approximately normal. The mean of the sampling distribution of $$ \hat{p} $$ is $$ 0.33 $$.

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