Answer :
Answer: [tex]\mu_{\hat{p}}=0.431\\\\ \sigma_{\hat{p}}=0.064[/tex]
Step-by-step explanation:
The mean and standard deviation of the sampling distribution of p is given by :-
[tex]\mu_{\hat{p}}=p\\\\ \sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}[/tex]
, where p= population proportion.
n= sample size.
Let p represent the sample proportion of Americans over the age of 65 that were male.
Given : The proportion of Americans over the age of 65 were male.
p= 43.1%=0.431
sample size : n= 60
Then, the mean and standard deviation of the sampling distribution of p will be :-
[tex]\mu_{\hat{p}}=p =0.431\\\\ \sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.431(1-0.431)}{60}}\\\\=\sqrt{0.0041}\approx0.064[/tex]
Hence, the mean and standard deviation of the sampling distribution of p :
[tex]\mu_{\hat{p}}=0.431\\\\ \sigma_{\hat{p}}=0.064[/tex]
