Answer:
The mean of the sampling distribution is 0.22 and the standard deviation is 0.0338.
Step-by-step explanation:
Central Limit Theorem:
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question, we have that:
[tex]p = 0.22, n = 150[/tex]
a) What are the mean and Standard deviation of the sampling distribution of p-hat
By the Central Limit Theorem,
Mean:
[tex]\mu = p = 0.22[/tex]
Standard deviation:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.22*0.78}{150}} = 0.0338[/tex]
The mean of the sampling distribution is 0.22 and the standard deviation is 0.0338.
