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6. (12 points) The following two equations were estimated to study the tradeoff between time spent sleeping and working and to look at other factors affecting sleep. The variables sleep and tonyor (total work) are measured in minutes per week and educ and age are measured in years: sleep =3,586.38-0.152fotwrk (38.98) (0.017) 1 = 706 R- =0.103 (6.1) sleep =3,638.25- 0.148 forwrk +11.13 edic + 2.20 age (112.28) (0.017) (5.88) (1.45) 1 =706 R- =0.113 (6.2) (a) Using equation (6.1), test the null hypothesis that toport has no effect on sleep against the alternative that topwork has a negative effect. Carry out the test at the 5% significance level (3 points). (b) Is educ individually significant at the 1% level against a two-sided alternative in equation (6.2)? Show your work (3 points). (c) Using equation (6.2), construct a 90% confidence interval for age (3 points). (d) Are educ and age jointly significant for determining time spent sleeping at the 5% level? Show your work (3 points)