Answer :
Answer:
[tex]\hat p \sim N (p , \sqrt{\frac{p(1-p)}{n}}) [/tex]
The mean is given by:
[tex] \mu_{\hat p} = 0.55[/tex]
And the deviation:
[tex] \sigma_{\hat p} =\sqrt{\frac{0.55*(1-0.55)}{953}}= 0.0161[/tex]
Step-by-step explanation:
For this case we assume that the true population proportion of Americans do not know that GOP stands for Grand Old Party is 0.55 and we select a random sample of n = 953 americans
For this case we assume that we satisfy the conditions to use the normal approximation for [tex]\hat p[/tex]
1) np >10 , n(1-p)>10
2) Independence
3) Random sample
4) The sample size is less than 10% of the population size
We assume that all the conditions are satisfied and the distribution for [tex]\hat p[/tex] would be:
[tex]\hat p \sim N (p , \sqrt{\frac{p(1-p)}{n}}) [/tex]
The mean is given by:
[tex] \mu_{\hat p} = 0.55[/tex]
And the deviation:
[tex] \sigma_{\hat p} =\sqrt{\frac{0.55*(1-0.55)}{953}}= 0.0161[/tex]