Question 1

Consider the estimated confidence interval for β2: Pr(3.21≤β2≤6.12=99%). How should this confidence interval be interpreted?

A. If 100 samples are drawn and 100 estimates for β2 derived, 99 such estimates will lie in the range 3.21 to 6.12.

B. There is a 1% chance that the true value of β2 lies outside the given bounds.

C. There is a 99% chance that the true value of β2 lies between 3.21 and 6.12.

D. In repeated sampling, if many confidence intervals like the one given above are estimated, 99% of them will contain the true β2. If the above interval encloses the true β2, then the slope estimate lies between 3.21 and 6.12.

E. We can be 99% confident that the true value of β2 is enclosed by the lower limit 3.21 and the upper limit 6.12.

Question 2

The ............. is/are used to construct confidence intervals around OLS parameters.

A. standard errors of β1 and β2

B. population regression function

C. standardized normal distribution

D. β^1−β1se(β^1) and β^2−β2se(β^2)

E. confidence limits

Question 3

How should the slope estimate of the following regression be interpreted (where wage is hourly wage and educexp is household average annual expenditure on education)?
ln(wage)=11.4+8.13ln(educexp)

A. When education expenditure increases by 1, on average, hourly wages increase by 8.13.

B. When education expenditure increases by 1 unit, on average, hourly wages increase by 8.13%.

C. When education expenditure increases by 1%, on average, hourly wages increase by 8.13 units.

D. When education expenditure increases by 1 unit, on average, hourly wages increase by 8.13 units.

E. When education expenditure increases by 1%, on average, hourly wages increase by 8.13%

Question 4

The Gauss-Markov theorem states that...

A. ordinary least squares estimators are always BLUE.

B. given the CLRM assumptions, ordinary least squares estimators are unbiased, low variance and consistent.

C. ordinary least squares estimators are better than parameter estimators.

D. given the CLRM assumptions, ordinary least squares estimators are BEST.

E. given the CLRM assumptions, ordinary least squares estimators have minimum variance among all unbiased linear estimators.

Question 5

Observations on years of education and hourly wages are sampled for 32 individuals and the regression wage=f(education) yields estimates β^1=12.5 and β^2=3.7. At α=0.01 what is the critical value for a left-tailed test of β2?

A. none of the answers provided are correct because a left-tailed t-test has a negative critical value.

B. 2.750

C. 5%

D. 1.697

E. 2.457

Question 6

If the test statistic value lies within the acceptance region it implies that...

A. the computed test statistic is, in absolute terms, larger than the critical value.

B. the null cannot be rejected.

C. the alternative hypothesis is false.

D. the alternative hypothesis is preferred.

E. the null hypothesis is true.

Question 7

When doing hypothesis testing, selecting a value for α is equivalent to...

A. choosing the probability of a Type I error.

B. choosing between a one-tailed and two-tailed test.

C. reducing the probability of a Type II error.

D. the test-statistic value.

E. choosing the critical value.

Question 8

Choose the correct statement below.

A. OLS minimises the sum of the residuals u^i.

B. OLS minimises the distance between the error terms and the regression line.

C. OLS minimises the squared distance between Yi and Y^i.

D. OLS minimises the sum of squared differences between the observed and estimated Yi.

E. OLS minimises each deviation between Yi and Y^i.

Question 9

Observations on years of education and hourly wages are sampled for 20 individuals and the regression wage=f(education) yields estimates β^1=12.5, β^2=3.7, and σ^=22.3. When doing a two-tailed hypothesis test on β2 with significance level of α=0.01, what would the critical t-value be?

A. 3.61

B. 2.11

C. none of the options provided are correct.

D. 2.552

E. 2.878

Question 10

When conducting a hypothesis test, the choice between a one-tailed or two-tailed test will depend on....

A. whether or not the direction of the statistical deviation from the null hypothesis value is important.

B. which test permits you to accept the null hypothesis.

C. which test allows you to reject the null hypothesis.

D. which ever gives you the desired result.

E. whether it is a t-test or a χ2-test

Question

Question 1

Consider the estimated confidence interval for β2: Pr(3.21≤β2≤6.12=99%). How should this confidence interval be interpreted?

A. If 100 samples are drawn and 100 estimates for β2 derived, 99 such estimates will lie in the range 3.21 to 6.12.
B. There is a 1% chance that the true value of β2 lies outside the given bounds.
C. There is a 99% chance that the true value of β2 lies between 3.21 and 6.12.
D. In repeated sampling, if many confidence intervals like the one given above are estimated, 99% of them will contain the true β2. If the above interval encloses the true β2, then the slope estimate lies between 3.21 and 6.12.
E. We can be 99% confident that the true value of β2 is enclosed by the lower limit 3.21 and the upper limit 6.12.

Question 2

The ............. is/are used to construct confidence intervals around OLS parameters.

A. standard errors of β1 and β2
B. population regression function
C. standardized normal distribution
D. β^1−β1se(β^1) and β^2−β2se(β^2)
E. confidence limits

Question 3

How should the slope estimate of the following regression be interpreted (where wage is hourly wage and educexp is household average annual expenditure on education)?

ln(wage)=11.4+8.13ln(educexp)

A. When education expenditure increases by 1, on average, hourly wages increase by 8.13.
B. When education expenditure increases by 1 unit, on average, hourly wages increase by 8.13%.
C. When education expenditure increases by 1%, on average, hourly wages increase by 8.13 units.
D. When education expenditure increases by 1 unit, on average, hourly wages increase by 8.13 units.
E. When education expenditure increases by 1%, on average, hourly wages increase by 8.13%

Question 4

The Gauss-Markov theorem states that...

A. ordinary least squares estimators are always BLUE.
B. given the CLRM assumptions, ordinary least squares estimators are unbiased, low variance and consistent.
C. ordinary least squares estimators are better than parameter estimators.
D. given the CLRM assumptions, ordinary least squares estimators are BEST.
E. given the CLRM assumptions, ordinary least squares estimators have minimum variance among all unbiased linear estimators.

Question 5

Observations on years of education and hourly wages are sampled for 32 individuals and the regression wage=f(education) yields estimates β^1=12.5 and β^2=3.7. At α=0.01 what is the critical value for a left-tailed test of β2?

A. none of the answers provided are correct because a left-tailed t-test has a negative critical value.
B. 2.750
C. 5%
D. 1.697
E. 2.457

Question 6

If the test statistic value lies within the acceptance region it implies that...

A. the computed test statistic is, in absolute terms, larger than the critical value.
B. the null cannot be rejected.
C. the alternative hypothesis is false.
D. the alternative hypothesis is preferred.
E. the null hypothesis is true.

Question 7

When doing hypothesis testing, selecting a value for α is equivalent to...

A. choosing the probability of a Type I error.
B. choosing between a one-tailed and two-tailed test.
C. reducing the probability of a Type II error.
D. the test-statistic value.
E. choosing the critical value.

Question 8

Choose the correct statement below.

A. OLS minimises the sum of the residuals u^i.
B. OLS minimises the distance between the error terms and the regression line.
C. OLS minimises the squared distance between Yi and Y^i.
D. OLS minimises the sum of squared differences between the observed and estimated Yi.
E. OLS minimises each deviation between Yi and Y^i.

Question 9

Observations on years of education and hourly wages are sampled for 20 individuals and the regression wage=f(education) yields estimates β^1=12.5, β^2=3.7, and σ^=22.3. When doing a two-tailed hypothesis test on β2 with significance level of α=0.01, what would the critical t-value be?

A. 3.61
B. 2.11
C. none of the options provided are correct.
D. 2.552
E. 2.878

Question 10

When conducting a hypothesis test, the choice between a one-tailed or two-tailed test will depend on....

A. whether or not the direction of the statistical deviation from the null hypothesis value is important.
B. which test permits you to accept the null hypothesis.
C. which test allows you to reject the null hypothesis.
D. which ever gives you the desired result.
E. whether it is a t-test or a χ2-test

Accepted Answer

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