The dataset HomesForSale has data on houses available for sale in three Mid-Atlantic states (NY, NJ, and PA). For this exercise we are specifically interested in homes for sale in New York and New Jersey. We have information on 30 homes from each state and observe the proportion of homes with more than three bedrooms. We find that 26.7% of homes in NY (p̂_NY) and 63.3% of homes in NJ (p̂_NJ) have more then three bedrooms.

(a) Is the normal distribution appropriate to model this difference?

(b) Test for a difference in proportion of homes with more than three bedrooms between the two states and interpret the result.