Describe the sampling distribution of p Assume the populatio

Describe the sampling distribution of p. Assume the population is 20,000. N=700, p=0.8

Solution

It is given that from the sample, sample proportion p = 0.8 and the sample size N = 700.

Sampling distribution of p is closely related to the Binomial Distribution with N=700 and p=0.8. The only difference is that Binomial Distribution deals with the number of Successes (X), but p deals with the proportion of Successes in the sample (X/N).

However, when N is fairly large, like in this case, p is approximated to a Normal DIstribution with mean = p= 0.8

and variance = p(1-p)/N = 0.8*0.2/700 = 1/4375 = 0.00022857