A food manufacturing company is interested in modeling whether people prefer x1= Type A or Type B hotdog buns with their hot dogs. They also want to control for x2= different amounts of sodium in the hot dogs themselves and are testing the hot dog buns at a variety of sodium contents, giving each taster both a hot dog and a bun with no condiments.The response variable is y= perceived taste of the bun, on a scale of 1 to 10.

(a) In order to find out whether Type A or Type B is preferred, is it necessary to have an interaction term? Why or why not?

(b) Develop a linear model for this study, interpreting all parameters in the context of the problem. Write down your hypotheses to be testing in terms of your model parameters. (You don't have any data to conduct the test; just write down the hypotheses.)

(c) Whether or not you added an interaction term above, assume now that it was added and it is statistically significant. How should we interpret this interaction in context?