STT 201, Sections 7--11 UNIT 4
Example Multiple Choice Questions
1-4. For each of the following testing situations, give the p-value of the observed test statistic. Pick the closest.
1. Two-sample t-test of H0: 1 - 2 0 versus Ha: 1 - 2 < 0, sample sizes n1 = 12, n2 = 10, tobs = 1.38.
Adopt the conservative approach to the degrees of freedom.
(a) .10 (b) .05 (c) .20 (d) .50 (e) .90
2. Two-sample (large samples) z-test of H0: 1 - 2 0 v. Ha: 1 - 2 > 0 if p1 = .47, p2 = .33 and zobs =
1.15.
(a) .085 (b) .071 (c) .054 (d) .125 (e) .101
3. A categorical variable y has five levels. Two populations are tested for having the same distribution of y
using large samples drawn from each population and 2obs = 11.12.
(a) .085 (b) .071 (c) .054 (d) .025 (e) .037
4. A categorical variable y has three levels. Four populations are tested for having the same distribution of y
using large samples drawn from each population and 2obs = 2.20.
(a) .085 (b) .001 (c) .050 (d) .900 (e) .100
5-6. A researcher administered a reading comprehension test to each of 16 subjects before and after a special
course that each subject took to improve reading comprehension. The researcher set the hypotheses H0: d 0
and Ha: d > 0 where d denotes difference (improvement). The summary of the data is given below.
Descriptive Statistics
N Mean Standard deviation
Before 16 52.8 9.3
After 16 56.8 8.1
Difference 16 4.0 7.6
5. What is the value of tobs for testing H0?
(a) 2.11 (b) 7.6 (c) 0.45 (d) 2.00 (e) 4.0
6. What is the p-value of tobs?
(a) .10 (b) .05 (c) .025 (d) .01 (e) .005
7-12. A veterinarian believes that the rate of hip dysplasia in Boxers (breed of dog) is less than the rate hip
dysplasia in American Bulldogs (breed of dog) and decides to test the hypothesis H0: 1-2 0 v. Ha: 1-2 < 0. A
random sample of 80 Boxers has 8 dogs with hip dysplasia. A random sample of 140 American Bulldogs has 21
dogs with hip dysplasia.
7. What is the standard error of the estimate p1 – p2 used in calculating the CI for 1 - 2?
(a) .085 (b) .071 (c) .045 (d) .037 (e) .101
8. What is the 99% CI estimate of the difference in population rates 1 - 2?
(a) -.05 .12 (b) -.05 .07 (c) -.05 .09 (d) -.05 .20 (e) -.05 .17
9. What is the standard error of the estimate p1 – p2 used in calculating the z-test statistic? (Hint: This is the
denominator of z-test statistic.)
(a) .085 (b) .071 (c) .064 (d) .047 (e) .101
10. Compute the value zobs of the z-test statistic.
(a) 0.52 (b) -0.90 (c) 1.96 (d) –1.06 (e) -1.96
11. What is the p-value of the test statistic zobs that is appropriate for this test? Pick the closest.
(a) 0.30 (b) 0.18 (c) 0.14 (d) 0.05 (e) 0.025
12. What decision is reached at 2% level of significance?
(a) reject the null hypothesis (b) retain the null hypothesis
