ISC-207, Summer, 2013, Statistics, Dr. Agarwal
Quiz-4 (Chapters 6 and 7, ANOVA and Categorical Data Analysis)
Name: ______Solutions_______________
Student ID (last four digits only) ________________
1. (0.5 pts.) If for some ANOVA experiment, suppose the test statistic value is 4.13 and the
critical value at alpha of 0.05 is say 4.12, you would
A. Reject the null hypothesis at alpha 0.05
B. Fail to reject the null hypothesis at alpha 0.05
C. It depends on the number of experimental data points
D. It depends on the number of groups in the experiment
2. (0.5 pts.) An ANOVA experiment involves 4 groups and has 24 experimental units or data
points. If I want to test my hypothesis at a significance level of 0.10, what should be the
critical value to use for my test?
A. 4.94
C. 2.38
B. 4.43
D. 3.10
3. (0.5 pts.) What is P(F < 5.57) for numerator dof = 2, and denom. dof =25?
A. 0.10
B. 0.90
C. 0.99
D. Depends on the significance level
4. (1 pt.) Say I perform two experiments to test the difference between the means of a variable
in 4 different populations (or groups). In the first experiment, I find that the Between-Group
MS = 2000 and the Within-Group MS = 500 and in the second experiment I find that the
Between-Group MS = 1000 and Within-Group MS = 200. In which of the two experiments are
the four population means more likely to be different?
A. The First Experiment
B. The Second Experiment (F value of second exper is 5. F value of first exper is 4)
C. There is not enough information given to answer this question
D. It depends on the significance level
5. (1 pt.) If my hypotheses look like this: H0: µ1 = µ2 vs. Ha: µ1 ≠ µ2, which type of test can be used
to test this hypothesis?
A. T-TEST or an ANOVA Test
B. T-TEST but not ANOVA
C. ANOVA but no T-Test
D. None of the above
6. (1 pt.) In an ANOVA test, whenever the critical value of F is higher than the test statistic value
F, the corresponding p-value is less than the alpha value. True/False
7. (0.5 pts.) The probability: P(χ2> 18.307) for df = 10 is ____0.05_________
8. (0.5 pts.) The probability: P(χ2< 39.997) for df = 20 is _____0.995________
Suppose a partial ANOVA table looks as follows: Assume α = 0.05
Source
SS
df
MS
F
Crit-F
Between Group
24
4
6
3
2.87
Within Group
40
20
2
Total
64
24
9. (1 pt.) What is the F value? _____3_______________
10. (0.5 pt.) What is Crit-F at α = 0.05? ______2.87________________
11. (0.5 pt.) In the above question, assume that your null hypothesis is that the means of all
groups is the same? Your decision about the null hypothesis at α = 0.05 is:
a. Fail to reject the null hypothesis
b. Reject the null hypothesis
c. To answer this question, we also need to know the p-value
12. The data below shows the age-group and the favorite type of music of 100 randomly selected
people. Test the claim that age-group and favorite music type are dependent of each
other. Use alpha = 0.025.
Age-Group
15 – 21
21 – 30
Sum
Country
20
30
50
Rock
30
20
50
Sum
50
50
100
E = 50*50/100 = 25 for each cell
(O-E)^2/E = 5^2/25 = 1 for each cell
(1.5 pts.) Compute the test statistic. ____1+1+1+1 = 4_______
13. (0.5 pt.) For the above test of independence, what is the critical value (alpha = 0.025)?
5.024
14. (0.5 pt.) What would be your decision in the above hypothesis test at alpha of 0.025?
A. Reject the Null
B. Fail to reject the Null
C. Not enough information to make a decision
D. Depends on the alternate hypothesis
15. (0.5 pt.) Please state your conclusion for the above hypothesis test:
There is not sufficient evidence at a significance level 0.025 that the favorite music type and
age group are dependent on each other.
16. An experiment with k = 3 categories and n = 200 produced the data shown in the following
table. We are interested in the null hypothesis that p1 = 0.25, p2= 0.25 and p3= 0.50 against
the alternate hypothesis that the proportions are different than specified in the null
hypothesis. We get the following data for testing this hypothesis:
Cell
1
2
3
ni (O)
60
60
80
Exp (E)
50
50
100
(O-E)
10
10
-20
(O-E)^2
100 100
400
(O-E)^2/E
2
2
4
(1.5 pts.)Compute the relevant test statistic to test the hypothesis. Type your answer up to one
decimal place. (Please put a box around your final answer)
test statistic = 2+2+4 = 8
17. (0.5 pt.)At a required significance level of 0.025, what is the rejection region to reject the null
hypothesis for the above question?
χ2 >= 7.378
18. (0.5 pts.) What would be your decision in the above hypothesis test at 0.025 significance
level?
A. Reject the Null
B. Fail to reject the Null
C. Not enough information to make a decision
D. Depends on the alternate hypothesis
(0.5 pt.) State your conclusion about the above hypothesis test.
There is sufficient evidence at a significance level of 0.025 that the proportions p1, p2 and p3
are not 0.25, 0.25 and 0.50 respectively.
19. (1 pt.) The following sample data for two populations is collected. If I perform a one-tailed
hypothesis that the mean of second population is greater than the mean of the first
population
2
4
5
5
4
6
3
5
4
7
6
Suppose the t-test gives a p-value of 0.051. Which of the following is true?
A. The null can be rejected at significance level of 0.10 but not at 0.05
B. The null can be rejected at significance level of 0.05 as well as 0.10
C. The null can be rejected at significance level of 0.05 but not at 0.10
D. The null can be rejected neither at significance level of 0.05 nor at 0.10
20. (0.5 pts.) The rejection region for a one-way χ2 test of a null hypothesis p1= p2= . . .= pk if k = 9
and α = 0.05 is:
A. χ2>15.507
B. χ2>16.919
C. χ2<16.919
D. χ2<15.507