A real estate company has been provided with a portfolio of town homes and single family homes at Tahoe Keys in California. The company surveys a nearby affluent town of 25,000 households to determine...

A real estate company has been provided with a portfolio of town homes and single family homes at Tahoe Keys in California. The company surveys a nearby affluent town of 25,000 households to determine which form of residence is preferred as a vacation home, so they can target their marketing accordingly. The company took a sample of 500 of these households. It turns out only 79 households preferred single family residences as a vacation home over town homes.

(a) Calculate the proportion of households in the town who prefer town homes as a vacation home.

(b) About how far off to you expect this estimate to be off?

(c) Calculate the 99 % confidence interval for the expected value.