A1. Which of the following is the correct definition of the p-value of a hypothesis test?
A. The minimum significance level at which the null hypothesis can be
B. The maximum significance level at which the null hypothesis can be
C. The probability of rejecting the null hypothesis when the null is true.
D. The probability of failing to reject the null hypothesis when the null is true.
E. The probability of rejecting the null hypothesis when the null is false.
A2. A statistician has carried out a survey on a random sample of 25 subjects. Following the collection of data, a one-tail hypothesis test has been carried out for the null hypothesis that the population mean is zero, against an alternative of a positive population mean. The p-value is 0.05. This indicates that:
A. The null hypothesis can be rejected at the 0.01 level.
B. The test statistic is 1.7109.
C. The test statistic is 2.0639.
D. The null hypothesis cannot be rejected at the 0.1 level.
E. Both A and D.
A3. In a hypothesis test, what happens to 1-, the power of the test, when , the significance level, is reduced?
A. The power is increased.
B. The power is unaltered.
C. The power is reduced.
D. The answer depends on the value of .
E. The answer depends upon the form of the alternative hypothesis.
A4. Which of the following statements is FALSE?
A. The significance level of a hypothesis test is the probability of committing a
Type I error.
B. If a null hypothesis is rejected at the 0.05 level, then it must also be rejected at the 0.01 level.
C. If the p-value is 0.025, the null hypothesis is accepted at the 0.01 level but the null hypothesis is rejected at the 0.05 level.
D. If the p-value is 0.075, the null hypothesis is rejected at the 0.1 level but the null hypothesis is accepted at the 0.05 level.
E. All of the above.
A5. Which of the following is NOT a necessary assumption underlying the test for the difference between two population means with small independent samples?
A. The means of the populations are the same.
B. The variances of the populations are the same.
C. The samples are randomly selected.
D. The populations are normally distributed.
E. Both A and B.
A6. An estimator is consistent if:
A. The expected value of the estimator corresponds to the true value of the
B. The estimator gives the same answer, regardless of the composition of the
C. The variance of the estimator is no larger than the variance of any other
D. The sampling distribution of the estimator converges to a normal distribution
as the sample size increases.
E. The sampling distribution of the estimator converges onto the true value of the
parameter as the sample size increases.
A7. Using a sample of 30 observations, a study found a sample correlation of xy ˆ = 0.41
between the proportion of women on a company’s board of directors, and its
profitability. Which of the following statements is TRUE?
A. Companies with a higher proportion of female directors are typically more
B. Companies with a higher proportion of female directors are typically less
C. There is no evidence of an association between the proportion of female
directors and profitability.
D. Each additional female director adds 0.41% on average to the company’s
E. Both A and D.
A8. In a logit regression:
A. The discrete dependent variable can take three or more numerical values, and
the ordering or ranking of the numerical values is meaningful.
B. We observe a latent variable, whose value provides an indication of the
probabilities for the discrete outcomes.
C. The Ordinary Least Squares (OLS) estimators of the logit regression
coefficients follow a logistic distribution.
D. The dependent variable is discrete and binary.
E. Both C and D.
A9. In the estimation of a two-variable linear regression model i 1 2 i i y x u using
20 observations, a researcher has obtained ˆ 4.21
2 and se(ˆ ) 2.16 2 . Which of the
following statements is TRUE?
is not significantly different from zero in a two-tail test at the 0.05
is significantly different from zero in a one-tail test at the 0.05 significance
C. The p-value for a test of H0:2=0 against H1:2>0 is greater than 0.01.
D. The p-value for a test of H0:2=0 against H1:20 is less than 0.1.
E. All of the above.
A10. A multiple regression model with k=3 regression coefficients (including the intercept)
was estimated using 30 observations. The following results were obtained:
(y y) 120 2
i , (yˆ y) 45 2
i , e 75 2
i . Which of the following statements is
A. The goodness-of-fit for this regression is 0.625.
B. The goodness-of-fit for this regression is 0.375.
C. An F-test for the joint significance of the explanatory variables produces a test
statistic of 8.1, which is significant at the 0.05 level.
D. Both A and C.
E. Both B and C.