Question

Consider the following model:

Y_i = β₀ + β₁(X₁)_i + β₂(X₂)_i + β₃(X₃)_i + β₄(X₄)_i + u_i

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 8^th 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.	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.
	b.	Estimated t-statistics for β3 and β4 would not be the best way to test this hypothesis.
	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 no 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 5% level of significance you would conclude that parental attributes have an impact on test scores.

Answer 1

We use the t test to obtain the significance of the individual independent variables. As we are given here that the t statistic values obtained are: 3.5 and 4.71, therefore the p-value for the test here are computed for the 2 variables as: (as this is a two tailed test )

For n - 1 = 4999 degrees of freedom, we

p₁ = 2P( t₄₉₉₉ > 3.5) = 2*0.0002 = 0.0004

p₂ = 2P(t₄₉₉₉ > 4.71) = approx. 0

As the p-values here are both less than 0.05 and even 0.01, therefore both the t tests are significant and we can reject the null hypothesis for both the tests here which means that both the individual variables are significant here.

Therefore A is the correct answer here.

Note that D is also correct, but 1% level of significance given more significance for the test here.