Question

Consider the following model:

Yi = β0 + β1(X1)i + β2(X2)i + β3(X3)i + β4(X4)i + ui

Where:

Y = Score in Standardized Test

X1 = Student IQ

X2 = School District

X3 = Parental Education

X4 = Parental Income

The data for 5,000 students was collected via a simple random sample of all 8th graders in New Jersey.  Suppose you want to test the hypothesis that parental attributes have no impact on student achievement.  Which of the following is most accurate?

a.
Estimated t-statistics for β3 and β4 would not be the best way to test this hypothesis.

b.
The best way to test this hypothesis is to look at the estimated t-statistics for β3 and β4.  Assuming they are 3.50 and 4.71, respectively, then at the 5% level of significance you would conclude that parental attributes have no impact on test scores.

c.
The best way to test this hypothesis is to look at the estimated t-statistics for β3 and β4.  Assuming they are 3.50 and 4.71, respectively, then at the 5% level of significance you would conclude that parental attributes have an impact on test scores.

d.
The best way to test this hypothesis is to look at the estimated t-statistics for β3 and β4.  Assuming they are 3.50 and 4.71, respectively, then at the 1% level of significance you would conclude that parental attributes have an impact on test scores.

Answer 1

Ans. (a) Estimated t statistics for B3 and B4 would not be the best way to test this hypothesis. This is because we now parents attributes include both parents education and parents income level , so we will be testing hypothesis for both B3 and B4 but not by the t- test of statistical significance , instead of that we have to use F- test which is a joint significance test , which will give us the best measure of the significance that whether any of the two attributes of parents are having a significant impact on children achievement or not . Also whether both attributes have no impact on children's achivement . So f- test is most appropriate for such hypothesis testing as it gives us joint significance. And t- test is inappropriate which this option claetky mention so it's the correct option

Rest of the option are incorrect. As they mention the t- test only .