A simple random sample of size $$ n=50 $$ is obtained from a population whose size is $$ \mathrm{N}=25,000 $$ and whose population proportion with a specified characteristic is $$ p=0.4 $$. (a) Describe the sampling distribution of $$ \hat{p} $$. Choose the phrase that best describes the shape of the sampling distribution. B. Approximately normal because $$ n \leq 0.05 \mathrm{~N} $$ and $$ n p(1-p) \geq 10 $$ C. Not normal because $$ n \leq 0.05 \mathrm{~N} $$ and $$ n p(1-p)

Question

A simple random sample of size $$ n=50 $$ is obtained from a population whose size is $$ \mathrm{N}=25,000 $$ and whose population proportion with a specified characteristic is $$ p=0.4 $$. (a) Describe the sampling distribution of $$ \hat{p} $$. Choose the phrase that best describes the shape of the sampling distribution. B. Approximately normal because $$ n \leq 0.05 \mathrm{~N} $$ and $$ n p(1-p) \geq 10 $$ C. Not normal because $$ n \leq 0.05 \mathrm{~N} $$ and $$ n p(1-p)<10 $$ D. Not normal because $$ n \leq 0.05 \mathrm{~N} $$ and $$ n p(1-p) \geq 10 $$ Determine the mean of the sampling distribution of $$ \hat{p} $$.

Huff Osborne · Accepted Answer

The sampling distribution of $$ \hat{p} $$ is approximately normal (Choice B). The mean of the sampling distribution of $$ \hat{p} $$ is $$ 0.4 $$.

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