Describe the Sampling Distribution of a Sample Proportion
-A simple random sample of size $\mathrm { n } = 450$ is obtained from a population whose size is $\mathrm { N } = 13,000$ and whose population proportion with a specified characteristic is $\mathrm { p } = 0.2$. Describe the sampling distribution of $\hat { p }$.
A) Approximately normal; $\mu _ { p } = 0.2 , \sigma p = 0.019$
B) Exactly normal; $\mu _ { \mathrm { p } } = 0.2 , \sigma _ { \mathrm { p } } = 0.019$
C) Approximately normal; $\mu _ { \mathrm { p } } = 0.2 , \sigma \mathrm { p } = 0.1109$
D) Binomial; $\mu _ { \mathrm { p } } = 90 , \sigma _ { \mathrm { p } } = 8.49$

Question

Quizplus · Accepted Answer

The sampling distribution of $\hat{p}$ is approximately normal due to the large sample size ($n = 450$) and the population proportion ($p = 0.2$). The mean of the sampling distribution, $\mu_{\hat{p}}$, equals the population proportion ($p = 0.2$). The standard deviation of the sampling distribution, $\sigma_{\hat{p}}$, is calculated using the formula $\sqrt{\frac{p(1-p)}{n}}$, which gives approximately 0.019 for $n = 450$ and $p = 0.2$.

Describe the Sampling Distribution of a Sample Proportion -A Simple n=450\mathrm { n } = 450n=450

Describe the Sampling Distribution of a Sample Proportion
-A Simple $\mathrm { n } = 450$