Describe the Sampling Distribution of a Sample Proportion
-A simple random sample of size $n = 1460$ is obtained from a population whose size is $\mathrm { N } = 1,400,000$ and whose population proportion with a specified characteristic is $\mathrm { p } = 0.57$. Describe the sampling distribution of $\hat { p }$.

A) Approximately normal; $\mu _ { \mathrm { p } } = 0.57 , \sigma _ { \mathrm { p } } = 0.013$
B) Exactly normal; $\mu _ { \mathrm { p } } = 0.57 , \sigma _ { \mathrm { p } } = 0.013$
C) Approximately normal; $\mu _ { \mathrm { p } } = 0.57 , \sigma _ { \mathrm { p } } = 0.1323$
D) Exactly normal; $\mu _ { \mathrm { p } } = 0.57 , \sigma _ { \mathrm { p } } = 0.1323$

Question

Describe the Sampling Distribution of a Sample Proportion
-A simple random sample of size $n = 1460$ is obtained from a population whose size is $\mathrm { N } = 1,400,000$ and whose population proportion with a specified characteristic is $\mathrm { p } = 0.57$. Describe the sampling distribution of $\hat  { p }$.

A) Approximately normal; $\mu _ { \mathrm { p } } = 0.57 , \sigma _ { \mathrm { p } } = 0.013$
B) Exactly normal; $\mu _ { \mathrm { p } } = 0.57 , \sigma _ { \mathrm { p } } = 0.013$
C) Approximately normal; $\mu _ { \mathrm { p } } = 0.57 , \sigma _ { \mathrm { p } } = 0.1323$
D) Exactly normal; $\mu _ { \mathrm { p } } = 0.57 , \sigma _ { \mathrm { p } } = 0.1323$

Quizplus · Accepted Answer

The sampling distribution of $\hat{p}$ is approximately normal due to the large sample size (n = 1460), which satisfies the condition for the Central Limit Theorem. The mean of the sampling distribution, $\mu_{\hat{p}}$, is equal to the population proportion $p = 0.57$. The standard deviation of the sampling distribution, $\sigma_{\hat{p}}$, is calculated using the formula $\sqrt{\frac{p(1-p)}{n}}$, which gives approximately 0.013 when $p = 0.57$ and $n = 1460$.

Describe the Sampling Distribution of a Sample Proportion -A Simple n=1460n = 1460n=1460

Describe the Sampling Distribution of a Sample Proportion
-A Simple $n = 1460$