A simple random sample of size $$ n=50 $$ is obtained from a population whose size is $$ N=25,000 $$ and whose population proportion with a specified characteristic is $$ p=0.4 $$. Coms (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 $$ N=25,000 $$ and whose population proportion with a specified characteristic is $$ p=0.4 $$. Coms (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 $$ \mathrm{np}(1-\mathrm{p}) \geq 10 $$ Determine the mean of the sampling distribution of $$ \hat{p} $$. $$ \mu_{\hat{p}}=0.4 $$ (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of $$ \hat{p} $$. $$ \sigma_{\hat{p}}=\square $$ (Round to six decimal places as needed.)

Johnson Herrera · Accepted Answer

The sampling distribution is approximately normal. The mean is 0.4 and the standard deviation is 0.069282.

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