The dataset HomesForSale has data on houses available for sale in three Mid- Atlantic states (NY, NJ, and PA) and California (CA). We are interested in the proportion of Mid- Atlantic houses that are larger than the mean US household size, which is approximately 2700 square feet. In the sample of 90 Mid-Atlantic homes for sale in HomesForSale, we see that 16 are larger then 2700 sqft.

(a) What is the sample proportion? Estimate the standard error of the sample proportion.

(b) Is the sample size large enough for the Central Limit Theorem to apply?

(c) Find and interpret a 95% confidence interval for the proportion of homes larger than the national mean in the Mid-Atlantic states.