Describe the Sampling Distribution of a Sample Proportion
-According to a study conducted in one city, $36 \%$ of adults in the city have credit card debts of more than $\$ 2000$. A simple random sample of $\mathrm { n } = 100$ adults is obtained from the city. Describe the sampling distribution of $\hat { \text { p} }$, the sample proportion of adults who have credit card debts of more than $\$ 2000$.
A) Approximately normal; $\mu _ { \mathrm { p } } = 0.36 , \sigma _ { \mathrm { p } } = 0.048$
B) Exactly normal; $\mu _ { \mathrm { p } } = 0.36 , \sigma _ { \mathrm { p } } = 0.048$
C) Approximately normal; $\mu _ { \mathrm { p } } = 0.36 , \sigma _ { \mathrm { p } } = 0.0023$
D) Binomial; $\mu _ { \mathrm { p } } = 36 , \sigma _ { \mathrm { p } } = 4.80$

Question

Quizplus · Accepted Answer

The sampling distribution of $\hat { \text { p} }$ is approximately normal due to the Central Limit Theorem, given a large enough sample size. The mean of the sampling distribution, $\mu _ { \mathrm { p } }$, is equal to the population proportion, which is $0.36$. The standard deviation of the sampling distribution, $\sigma _ { \mathrm { p } }$, is calculated using the formula $\sqrt{\frac{p(1-p)}{n}}$, which gives $\sqrt{\frac{0.36(1-0.36)}{100}} = 0.048$.

Describe the Sampling Distribution of a Sample Proportion -According to a Study

Describe the Sampling Distribution of a Sample Proportion
-According to a Study