Question

4) The following equation was estimated to explain sleeping patterns sleep = 3,638.25 -0,148 fotwork -11.13* educ+ 2.20 age (112.28) (0,017) (5.88) (1.45) n=706, R =0,113 a) (5 points) is either educ or age significant at the 5% level against a two-sided alternative? Show you work. b) (5 points) Dropping educ and age from the equation gives sleep = 3,586,38 -0.151 to work (38.91) (0,017) n=706, R =0,103 Are educ and age jointly significant in the original equation at the 5% level? Justify your answer.

Answer 1

- Sleep = 3 638.25 -0.148 To towork- 14.13 educt 220 * age Ho (a) Ho: P = 0 HI: Beto Hylomeosignificant) (significant) toBS = - the bz sel selba) = - 1.13 5.88 toBS. – – 1.89 whereas TCRIT - ta/20=700 - to.025, n= 70 6. (CRIT- 1.960 Acceptance toBS – – 1.89 region -1.9601 +1.960 Since to BS Lies - - 1.89 in Acceltance region of dicuram so we are not able to reject Ho: educ is insignificant

Hypothesis Ho: B3 = 0 Hi. Bo to ( insignificant) (significant) toBS = 33 Se (63) = 2.20 1045 = 1.517 ACRIT, 0.025, n = 7706 = 1.960 +1.960 again coc are not able To Reject . Accept Hot Ho" (Because I tops IC 1.960) -1.960 So age is insignificant (0) Hylomesis for checking whether cauc and age. Jointly Significant in the orginal Equation. as dropping The vanable and making Restrictions ich are valid or not so typothesis Ho restrictions are valid that is ß2 = P3=0 HI: restrictions are invalid that is pat B380 and to yor this we use the F- Statistics Hypothesis Testing

Where m= F Statistic is F = (Rur- &8) Im (1-Rur) | Ch-k) 1 where m= no. of Restrictions impose = no. of Parameters inclucling intercept Rur= 0.113 R = 00103 m = 2 K= 4 FOBS - (0.13 – 0. 103)/2 (1-0.113] | (706-41) 0.01/2 0.005 (0.887)/702 0.0012 – 3.8401 KTT a=5 h 2 707 = 2.9957 FERIT, 005, 2, 702 = 2.9957 3.846/ FOBS Lics in Rejection Region. So we find evidence that 2.9957 Ho can be rejected. So Restrictions are invalid So educ and age are Jointly significant.