12.14. Using software with the Housesdata set at the text website, conduct an ANOVA for y = house selling price with factors whether the house is new and whether number of bathrooms exceeds two.

(a) Using α = 0.05, test the hypothesis of no interaction between the factors in their effects on y.

(b) Assuming no interaction, conduct the test of the hypothesis that the population mean of y is the same for new and older homes, controlling for the bathrooms indicator.
Interpret.