Respuesta :
Answer:
The standard deviation of the sampling distribution will be 2 times larger with sample size 400.
Step-by-step explanation:
The standard deviation of the sampling distribution of the sample proportion is:
[tex]SD(\hat p)=\sqrt{\frac{ p(1-p)}{n}}[/tex]
For the sample size n₁ = 400 compute the standard deviation of sample proportion as follows:
[tex]SD_{1}(\hat p)=\sqrt{\frac{ p(1-p)}{n_{1}}}=\sqrt{\frac{ p(1-p)}{400}}=\frac{1}{20}\sqrt{ p(1-p)}[/tex]
For the sample size n₂ = 1600 compute the standard deviation of sample proportion as follows:
[tex]SD_{2}(\hat p)=\sqrt{\frac{ p(1-p)}{n_{2}}}=\sqrt{\frac{ p(1-p)}{1600}}=\frac{1}{40}\sqrt{ p(1-p)}[/tex]
So the relation between the two standard deviations is:
[tex]SD_{2}=\frac{1}{2} SD_{1}[/tex]
So the standard deviation for size 400 is 2 times larger than the standard deviation with size 1600.
Thus, the standard deviation of the sampling distribution will be 2 times larger with sample size 400.
