Deck 4: Interval Estimation and Hypothesis Testing

Question 1

)Which of the following cannot be an alternative hypothesis?

A) $\beta$ _k = 0
B) $\beta$ _k ≠ 0
C) $\beta$ _k > 0
D) $\beta$ _k < 0

Answer 1

$\beta$ _k = 0

Question 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)
You want to test the following hypothesis: H₀: $\beta$ ₂ = 12,H₁: $\beta$ ₂ ≠12.If you choose to reject the null hypothesis based on these results,what is the probability you have committed a Type II error?

A)between .05 and .10
B)between .01 and .025
C)between .02 and .05
D)It is impossible to determine without knowing the true value of $\beta$ ₂

Answer 2

It is impossible to determine without knowing the true value of $\beta$ ₂

Question 3

You want to test the hypothesis H₀: (c₁ $\beta$ ₁ + c₂ $\beta$ ₂)- c₀ = 0 and H₁: (c₁ $\beta$ ₁ + c₂ $\beta$ ₂)- c₀ ≠ 0
What test statistic should you use for the test?

A)
B)
C)
D) $\chi$ ²=( $\beta$ ₁- $\beta$ ₂)/se( $\beta$ ₁ + $\beta$ ₂)

Answer 3

Question 4

)For which alternative hypothesis do you reject H₀ if |t| ≤t _{( $\alpha$ /2 ,N-2)}?

A) $\beta$ _k = c
B) $\beta$ _k ≠ c
C) $\beta$ _k > c
D) $\beta$ _k < c

Question 5

)For which alternative hypothesis do you reject H₀ if t≤t _{( $\alpha$ ,N-2)}?

A) $\beta$ _k = c
B) $\beta$ 0_k ≠ c
C) $\beta$ _k > c
D) $\beta$ _k < c

Question 6

)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

Question 7

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 $\alpha$ for which you cannot reject the null hypothesis based on the data
D)The probability that the null hypothesis is true

Question 8

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: $\beta$ ₂ = 1,H₁: $\beta$ ₂ >12.If you choose to reject the null hypothesis based on these results,what is the probability you have committed a Type I error?

A)between .01 and .02
B)between .02 and .05
C)less than .005
D)It is impossible to determine without knowing the true value of $\beta$ ₂

Question 9

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).025
B).050
C).975
D).950

Question 10

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

A)reduce $\alpha$
B)increase $\alpha$
C)use a two-tailed test
D)increase the rejection region

Question 11

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 $\beta$ 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)

Question 12

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 $\beta$ 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)

Question 13

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).01
B).99
C).02
D).05

Question 14

You want to test the hypothesis H₀: (c₁ $\beta$ ₁ + c₂ $\beta$ ₂)- c₀ = 0 and H₁: (c₁ $\beta$ ₁ + c₂ $\beta$ ₂)- c₀ ≠ 0
If the null hypothesis is true,how will the test statistic be distributed?

A)t_{( $\alpha$ /2)}
B)N(0,1)
C)t_(N-2)
D) $\chi$ ² (_N-2 )

Question 15

Which of the following is not a component of a hypothesis tes?

A)null hypothesis
B)goodness-of-fit
C)test statistic
D)rejection region

Question 16

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: $\beta$ ₂ = 12,H1: $\beta$ ₂ ≠12.If you choose to reject the null hypothesis based on these results,what is the probability you have committed a Type I error?

A)between .05 and .10
B)between .01 and .025
C)between .02 and .05
D)It is impossible to determine without knowing the true value of $\beta$ ₂

Question 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 $\beta$ ₂ is positive.

Question 18

)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.