Answer:
[tex]\mu_{\hat{p}}=0.50\\\\\sigma_{\hat{p}}=0.0158[/tex]
Step-by-step explanation:
The probability distribution of sampling distribution [tex]\hat{p}[/tex] is known as it sampling distribution.
The mean and standard deviation of the proportion is given by :-
[tex]\mu_{\hat{p}}=p\\\\\sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}[/tex]
, where p =population proportion and n= sample size.
Given : According to a survey, 50% of Americans were in 2005 satisfied with their job.
i.e. p = 50%=0.50
Now, for sample size n= 1000 , the mean and standard deviation of the proportion will be :-
[tex]\mu_{\hat{p}}=0.50\\\\\sigma_{\hat{p}}=\sqrt{\dfrac{0.50(1-0.50)}{1000}}=\sqrt{0.00025}\\\\=0.0158113883008\approx0.0158[/tex]
Hence, the mean and standard deviation of the proportion for a sample of 1000:
[tex]\mu_{\hat{p}}=0.50\\\\\sigma_{\hat{p}}=0.0158[/tex]
