In: Economics
Questions 8-12 are related to the following:
Consider the following hypothesis test.
H₀: μ ≤ 42 H₁: μ > 42
The sample size is n = 110, and the sample mean is x̅ = 46.2 with the standard deviation s = 24.25
8.This test is:
A. A lower-tail test.
B. An upper-tail test.
C. A two-tail test.
D. A closed-interval test.
9. The test statistic is (if negative, use the absolute value),
A. 1.99
B. 1.89
C. 1.82
D. 1.71
10. The critical value for a 5 percent level of significance is:
A. 1.850
B. 1.752
C. 1.659
D. 1.566
11.The p-value for the test is approximately,
A. 0.023
B. 0.035
C. 0.057
D. 0.090
12.The test leads you to:
A. Not reject H₀ at a 5 percent, and do not reject H₀ at a 10 percent level of significance.
B. Not reject H₀ at a 5 percent, but reject H₀ at a 10 percent level of significance.
C. Reject H₀ at a 5 percent, but not reject H₀ at a 10 percent level of significance.
D. Reject H₀ at a 5 percent, and reject H₀ at a 10 percent level of significance.
8. The correct option would be
The null and alternate hypothesis suggests that we are interested in the question whether the mean is more than 42 (may or may not be the population mean). That is why the acceptance region of null would be on the left side, which would mean that the mean is not more than 42, and vice versa, the rejection region of the null would be on the right side, which would mean that the mean is indeed more than 42.
9. The correct option would be
The test would be done by the one sample t-test. The test statistic would be as or or or or .
10. The correct option would be
The critical value at 5% significance level would be as or .
11. The correct option would be
The p-value would be as , for X belonging to t-distribution with df=109, ie or .
12. The correct option would be
As can be seen, we have p-value less than 5%, and hence p-value is also less than 10%, meaning that we may reject the null at 5% and 10% significance level. In general, rejecting a null at 5% would mean rejecting the null at 10% too.