The dataset HomesForSale has data on houses available for sale in three Mid-Atlantic states (NY, NJ, and PA) as well as California (CA). In Exercise C.62 we see that in the sample of 90 Mid- Atlantic homes for sale, 16 are larger than the national average. In the sample of 30 California homes, 7 are larger than the national average.

(a) Is the normal distribution appropriate to model the proportion larger than the national average for Mid-Atlantic houses? California houses?

(b) Do we have sufficient evidence at a5%level that the proportion of Mid-Atlantic homes larger than the national average is less then 25%? Perform an appropriate test.

(c) Do we have sufficient evidence at a 5% level that the proportion of California homes larger than the national average is less than 25%? Perform an appropriate test  

Exercise C.62

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.