Question: The real estate assessor for a county government wants to study various characteristics of single-family houses in the county. A random sample of 70 houses was taken and the following data obtained: (1) Heated area of the houses (in sq. ft.) in the sample is \[\bar{X}\] = 1,759, s = 380, and (2) 42 houses have central air conditioning. (16 points as indicated)

Construct a 95% confidence interval estimate for the population proportion of single-family houses that have central air conditioning. (5 points)