In Problem 3 in Chapter 3, we estimated the equation sleep 5 3,638.25 2 .148 totwrk 2 11.13 educ 1 2.20 age 1112.282 1.0172 15.882 11.452 n 5 706, R2 5 .113, where we now report standard errors along with the estimates.

(i) Is either educ or age individually significant at the 5% level against a two-sided alternative?

Show your work.

(ii) Dropping educ and age from the equation gives sleep 5 3,586.38 2 .151 totwrk 138.912 1.0172 n 5 706, R2 5 .103.

Are educ and age jointly significant in the original equation at the 5% level? Justify your answer.

(iii) Does including educ and age in the model greatly affect the estimated tradeoff between sleeping and working?

(iv) Suppose that the sleep equation contains heteroskedasticity. What does this mean about the tests computed in parts (i) and (ii)?