Using the regression output for the food expenditure model shown in Figure 2.9:

(a) Construct a 95% interval estimate for b1 and interpret.

(b) Test the null hypothesis that b1 is zero against the alternative that it is not at the 5% level of significance without using the reported p-value. What is your conclusion?

(c) Draw a sketch showing the p-value 0.0622 shown in Figure 2.9, the critical value from the t-distribution used in (b), and how the p-value could have been used to answer (b).

(d) Test the null hypothesis that b1 is zero against the alternative that it is positive at the 5% level of significance. Draw a sketch of the rejection region and compute the p-value. What is your conclusion?