Answer: 0.0346
Step-by-step explanation:
Required formula : [tex]\sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}[/tex] , where p= population proportion
n= sample size.
Let p be the population proportion for successes .
As per given , we have
Null hypothesis : [tex]H_0: p_0=0.40[/tex]
n= 200
Standard deviation of [tex]\hat{p}[/tex] = [tex]\sigma_{\hat{p}}=\sqrt{\dfrac{0.40(1-0.40)}{200}}[/tex]
[tex]\sigma_{\hat{p}}=\sqrt{0.0012}[/tex]
[tex]\sigma_{\hat{p}}=0.0346410161514\approx0.0346[/tex]
Hence , the required standard deviation of [tex]\hat{p}[/tex] = 0.0346
