Question

According to a poll, 55% of Americans do not know that GOP stands for Grand Old Party (Time, October 17, 2011). Assume that this percentage is true for the current population of Americans. Let p^ be the proportion in a random sample of 895 Americans who do not know that GOP stands for Grand Old Party. Find the mean and standard deviation of the sampling distribution of p^ and describe its shape. Round your answer for the standard deviation to four decimal places.

The sampling distribution of p^ is:

Answer 1

Solution:
Given in the question
55% of americans do not know the GOP stands for Grand Old Paty.
So Population proportion P = 0.55
No. of sample = 895
The mean and standard deviation of the sampling distribution of P^ can be calculated as
mean of the sampling distribution = Population proportion = 0.55
Standard deviation of sampling distribution = sqrt(P*(1-P)/n)) = sqrt(0.55*(1-0.45)/895) = sqrt(0.55*0.45/895) = 0.0166
so mean and standard deviation of the sampling distribution sample proportion p^ is 0.55 and 0.0166 respectively.