Suppose a simple random sample of size n1000 is obtainedfrom

Suppose a simple random sample of size n=1000 is obtainedfrom a population whose size is n=1,000,000 and whose population proportion with a specified characteristics is p=0.42.

Describe the samplind distribution of p^

Solution

It has a mean of

u(p^) = 0.42.

Meanwhile, its standard deviation is given by

s(p^) = sqrt[p(1-p)(N-n)/(n(N-1))] = sqrt(0.42*(1-0.42)*(1000000-1000)/((1000*(1000000-1)) =

s(p^) = 0.015599892

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Thus, the sampling distribution has mean

u(p^) =0.42

and standard deviation of

s(p^) =0.015599892 [ANSWER]