A study was conducted to determine whether certain features could be used to explain variability in the prices of air conditioners." For a sample of nineteen air conditioners, the following regression was estimated: y-68.236.0023x + 19.729 +7.653x) R-84 (.005) (8.992) (3.082) where y Price (in dollars) x, Rating of air conditioner, in BTU per hour Xz Energy efficiency ratio xy-Number of settings The figures in parentheses beneath the coefficient estimates are the corresponding esti- mated standard errors.

(a) Find a 95% confidence interval for the expected increase in price resulting from an ad- ditional setting when the values of the rating and the energy efficiency ratio remain fixed.

(b) Test the null hypothesis that, all else being equal, the energy efficiency ratio of air conditioners does not affect their price against the alternative that the higher the en- ergy efficiency ratio, the higher the price.