Refer to the data of Example 12.7 with the data file Citydatr.

a. Find 95% and 99% confidence intervals for the expected change in the market price for houses resulting from a one-unit increase in the mean number of rooms when the values of all other independent variables remain unchanged.

b. Test the null hypothesis that, all else being equal, mean household income does not influence the market price against the alternative that the higher the mean household income, the higher the market price.