Question

Part A: What is the mean of a sampling distribution of a proportion when the population proportion is p=0.3 and the sample size n=1000?

Part B: N=100

a. 0.3

b. 0.03

c.30

d. 3

e. 300

Answer 1

solution:
Part A:
n=1000, p=0.3
By definition of central limit theorem, for a large sample ( n>=30)the sample mean is same as the population mean.
Therefore, sample proportion is same as the population proportion.
p^ = p =0.3
Part B:
N=100, p=0.3
By definition of central limit theorem, for a large sample ( n>=30)the sample mean is same as the population mean.
Therefore, sample proportion is same as the population proportion.
p^ = p =0.3
Answer: a) 0.3