Interval Estimation And Hypothesis Testing Ch.3 Exam Prep

File: Ch03, Chapter 3, Interval Estimation and Hypothesis Testing

Multiple Choice

1. Suppose you wish to construct a 95% confidence interval around an unknown parameter, . Further assume you have estimated a simple linear regression model using 1000 observations and have an estimate of , , with its standard error, . The formula you would use to construct the endpoints of the interval is _____.

a.

b.

c.

d.

2. You estimate a simple linear regression model using a sample of 62 observations and obtain the following results (estimated standard errors in parentheses below coefficient estimates):

y = 97.25 + 33.74 *x

(3.86) (9.42)

What are the endpoints of the interval estimator for ₂ with a 95% interval estimate?

a. (14.90, 52.58)

b. (24.32, 43.16)

c. (-3.58, 3.58)

d. (30.16,37.32)

3. You estimate a simple linear regression model using a sample of 25 observations and obtain the following results (estimated standard errors in parentheses below coefficient estimates):

y = 97.25 + 19.74* x

(3.86) (3.42)

What are the endpoints of the interval estimator for ₂ with a 98% interval estimate?

a. (-5.77, 25.51)

b. (16.32, 23.16)

c. (11.19, 28.29)

d. (12.90, 26.58)

4. You estimate a simple linear regression model using a sample of 62 observations and obtain the following results (estimated standard errors in parentheses below coefficient estimates):

y = 97.25 + 33.74* x

(3.86) (9.42)

You want to test the following hypothesis: H₀: ₂ = 12, H1: ₂ ≠12. If you choose to reject the null hypothesis based on these results, the probability you have committed a Type I error is _____.

a. between .05 and .10

b. between .01 and .025

c. between .02 and .05

d. impossible to determine without knowing the true value of ₂

5. You estimate a simple linear regression model using a sample of 62 observations and obtain the following results (estimated standard errors in parentheses below coefficient estimates):

y = 97.25 + 33.74* x

(3.86) (9.42)

You want to test the following hypothesis: H₀: ₂ = 12, H₁: ₂ ≠12. If you choose to reject the null hypothesis based on these results, the probability you have committed a Type II error is _____.

a. between .05 and .10

b. between .01 and .025

c. between .02 and .05

d. impossible to determine without knowing the true value of ₂

6. You estimate a simple linear regression model using a sample of 25 observations and obtain the following results (estimated standard errors in parentheses below coefficient estimates):

y = 97.25 + 19.74 *x

(3.86) (3.42)

You want to test the following hypothesis: H₀: ₂ = 1, H₁: ₂ >12. If you choose to reject the null hypothesis based on these results, the probability you have committed a Type I error is _____.

a. between .01 and .02

b. between .02 and .05

c. your chosen value of

d. impossible to determine without knowing the true value of ₂

7. Which of the following is not a component of a hypothesis test?

a. Null hypothesis

b. Goodness-of-fit

c. Test statistic

d. Rejection region

8. Rejecting a true null hypothesis _____.

a. is a Type I error

b. is a Type II error

c. should not happen if a valid statistical test is used

d. depends on the size of the estimation sample

9. For which alternative hypothesis do you reject H₀ if t≤t _(,N-2)?

a. _k = c

b. _k ≠ c

c. _k > c

d. _k < c

10. For which alternative hypothesis do you reject H₀ if |t| ≤t _{(,N-2)}?

a. _k = c

b. _k ≠ c

c. _k > c

d. _k < c

11. How do you reduce the probability of committing a Type I error?

a. Reduce 

b. Increase 

c. Use a two-tailed test

d. Increase the rejection region

12. In which case would testing the null hypothesis involve a two-tailed statistical test?

a. H₁: Incentive pay for teachers does affect student achievement.

b. H₁: Higher sales tax rates does not reduce state tax revenues.

c. H₁: Extending the duration of unemployment benefits does not increase the length of joblessness.

d. H₁: Smoking does not reduce life expectancy.

13. In testing H₀: ₂ = c using a .05 probability of a Type I error, you find a p-value of .38. What should you conclude?

a. H₀ is true, ₂ = c.

b. H₀ should be rejected and is unlikely to be true since the p-value < .50.

c. It is impossible to know for sure, but there is a .38 probability that ₂ = c.

d. There is not sufficient evidence to reject H₀, so we accept the hypothesis by default.

14. What does a p-value NOT tell you?

a. The size of the largest rejection region that would not contain the observed test statistic.

b. The probability that the null hypothesis is true and you would observe a test statistic more extreme than the one observed.

c. The highest value of  for which you cannot reject the null hypothesis based on the data.

d. The probability that the null hypothesis is true.

15. If you are performing a two-tailed test of significance and you find that the area to the left of |t_c| is .975, what is the p-value?

a. 0.025

b. 0.050

c. 0.975

d. 0.950

16. If you are performing a left-tailed significance test and find the area to the left of |t_c| is .99, what is the p-value?

a. 0.01

b. 0.99

c. 0.02

d. 0.05

17. When should a left-tailed significance test be used?

a. When economic theory suggests the coefficient should be positive.

b. When it allows you to reject the null hypothesis at a lower p-value.

c. When economic theory suggests the coefficient should be negative.

d. When you know the true value of ₂ is positive.

18. You want to test the hypothesis

H₀: (c₁ ₁ + c₂₂) – c₀ = 0 and H₁: (c₁ ₁ + c₂₂) – c₀ ≠ 0

What test statistic should you use for the test?

a.

b.

c.

d. ^__se__

19. You want to test the hypothesis

H₀: (c₁ ₁ + c₂₂) – c₀ = 0 and H₁: (c₁ ₁ + c₂₂) – c₀ ≠ 0

If the null hypothesis is true, how will the test statistic be distributed?

a. t_(/2)

b. N(0,1)

c. t_(N-2)

d. ^_{}