In Problem 3.3, we estimated the equation where we now re

Homewroklib Q&A #1270 - In Problem 3.3, we estimated the equation where we now re

In Problem 3.3, we estimated the equation

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.

 

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Step #1 of 3

(i) With , use the standard normal critical value ( from the table), which is for a two-tailed test at the level. The t-statistic is calculated as shown below: Since, Hence, researcher fails to reject at the level. Also, -statistic for age is calculated below: Hence, So, age is also statistically insignificant at the level. df = 706 − 4 = 702 df = 8 1.96 5% t − statistics = 5.88 −11.13 ≈ −1.89 ∣tefunc ∣ = 1.89 < 1.96 H0 : βedwe = 0 5% t t − statistics = 1.45 2.20 = 1.52 tage ≈ 1.52

Step #2 of 3

(ii) There is need to compute the -squared form of the statistic for joint significance: The critical value in the distribution from the table with denominator . Therefore, educ and age are jointly significant at the level In fact, the -value is about , and so educ and age are jointly significant at the level. (iii) No, the variables educ and age in the model does not greatly affect the estimated tradeoff between sleeping and working. These variables are jointly significant, but including them only changes the coefficient on totwrk from to . R F F − test = [ (702/2) 1 − .113 .113 − .103] ≈ 3.39 5% F2,702 df = 8 : cv = 3.00 5% (3.39 > 3.00). p 0.019 2% −0.15

Step #3 of 3

(iv) The standard t and F statistics that researcher used assume homoscedasticity, in addition to the other CLM assumptions. If there is heteroskedasticity in the equation, the tests are no longer valid and the results will be biased

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