2. Assume that the population proportion of adults having a college degree is 0.35. A random sample of 200 adults is to be selected to test this claim.

Question

A) What is the shape, mean, and standard deviation of the sampling distribution of the sample proportion for samples of size 200?
B) What is the probability that the sample proportion will fall within 2% of the population proportion?
C) Answer part B if the sample size were increased to 500 adults. How does the answer to part C differ from part B, and why?

Answer 1

I'll give you a few hints.

Use the approximation to the binomial distribution.

Your values are the following:
p = .35, q = 1 - p = .65, n = 200

Find mean and standard deviation.
mean = np = (200)(.35) = ?
sd = √npq = √(200)(.35)(.65) = ?

Determine two z-scores.
z = -.02/(sd/√n)
z = .02/(sd/√n)

Once you have the z-scores, you should be able to determine the probability between the two z-scores using a z-table.

For part C), just increase the sample size and recalculate.

I hope this will help get you started.

Answer 2

mean 114
sd=8.608