To investigate the tradeoff between time to work and time to sleep, the followin

Question

To investigate the tradeoff between time to work and time to sleep, the following equation is estimated: sleep^cap = 3, 600 + 0.128totwrk - 10.08educ + 2.10age (1132.14) (0.016) (5.58) (1.35) n = 700, R^2 = 0.112 Standard errors are in the parentheses. (1) Is either educ or age individually significant at the 5% level? Show your work. (2) Dropping educ and age from the equation gives sleep^cap = 3, 780 - 0.104totwrk (52.04) (0.012) n = 700, r^2 = 0.098 Are educ and age Jointly significant in the original equation at the 5% level? Justify your answer.

Explanation / Answer

a) df= 700 – 4= 696, standard normal critical value (df=), = 1.96 for a two-tailed test at the 5% level.

educ: t-stat is -10.08/5.58 = -1.80, so -1.80< 1.96, and we fail to reject H0:educ= 0 at the5% level. Therefore,the coefficient for educ is not statistically significant at the 5% level.

age: t-stat =2.10/1.35 = 1.56 < 1.96 for the coefficient on age, so the coefficient for age is not statistically significant at the 5% level either.

b)

We could to compute the R2-form of the F statistic for joint significance.

F = (0.1120.098/10.112) * (696/2) = 5.4865.

The 5% critical value is the F2,696 distribution can be obtained with a denominator df = : 3.00.

Therefore, educ and age are jointly significant at the 5% level. (In fact, the p value is about 0.00432, and so educ and age are jointly significant at the 0.5% level).

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