Because of the high cost of energy, home-owners in northern climates need to find ways to cut their heating costs. A building contractor wanted to investigate the effect on heating costs of increasing the insulation. As an experiment, he located a large sub-development built around 1970 with minimal insulation. His plan was to insulate some of the houses and compare the heating costs in the insulated homes with those that remained un-insulated.

However, it was clear to him that the size of the house was a critical factor in determining heating costs. Consequently, he found 16 pairs of identical sized houses ranging from about 1,200 to 2,800 square feet. He insulated one house in each pair (levels of R20 in the walls and R32 in the attic) and left the other house unchanged. The heating cost for the following winter season was recorded for each house.

a. Do these data allow the contractor to infer at the 10% significance level that the heating cost for insulated houses is less than that for the un-insulated houses?

b. Estimate with 95% confidence the mean savings due to insulating the house.

c. What is the required condition for the use of the techniques in parts (a) and (b)?