Question: A normally distributed population has a mean of 40 and a standard deviation of 12. What does the central limit theorem say about the sampling distribution of the mean if samples of size 100 are drawn from this population?
a. In a random sample of 500 observations, we found the proportion of successes to be 48% Estimate with 95% confidence the population proportion of successes.
b. Repeat part (a) with n = 200
c. Repeat part (a) with n = 1000
d. Describe the effect on the confidence interval estimate of increasing the sample size.