Download Quiz-4 - Anurag Agarwal

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.) 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 0.01, what should be the
critical value to use for my test?
A. 4.43
C. 2.38
B. 4.94
D. 3.10
2. (0.5 pts.) If for some ANOVA experiment, suppose the test statistic value is 4.11 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 (because test stat is < critical value)
C. It depends on the number of experimental data points
D. It depends on the number of groups in the experiment
3. (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 = 1000 and the Within-Group MS = 200 and in the second experiment I find that the
Between-Group MS = 2000 and Within-Group MS = 500. In which of the two experiments are
the four population means more likely to be different?
A. The First Experiment (because the F value of first exper is 5 and of second exper is 4)
B. The Second Experiment
C. There is not enough information given to answer this question
D. It depends on the significance level
4. (0.5 pts.) What is P(F <2.53) for numerator dof = 2, and denom. dof =25?
A. 0.10
B. 0.90
C. 0.99
D. Depends on the significance level
Suppose a partial ANOVA table looks as follows: Assume α = 0.10
Source
SS
df
MS
F
Crit-F
Between Group
20
4
5
2.5
2.25
Within Group
40
20
2
Total
60
24
5. (1 pt.) What is the F value? ______2.5______________
6. (0.5 pt.) What is Crit-F at α = 0.10? _______2.25_______________
7. (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 = 0.10 is:
a. Reject the null hypothesis
b. Fail to reject the null hypothesis
c. To answer this question, we also need to know the p-value
8. (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 but not ANOVA
B. T-TEST or an ANOVA Test
C. ANOVA but no T-Test
D. None of the above
9. (1 pt.) The following sample data for two populations is collected. Suppose I have a onetailed 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 0.05 as well as 0.10
B. The null can be rejected at significance level of 0.05 but not at 0.10
C. The null can be rejected at significance level of 0.10 but not at 0.05
D. The null can be rejected neither at significance level of 0.05 nor at 0.10
10. (1 pt.) In an ANOVA test, whenever the critical value of F is less than the test statistic value F,
the corresponding p-value is less than the alpha value. True/False
11. (0.5 pts.) The probability: P(χ2> 39.997) for df = 20 is ___0.005__________
12. (0.5 pts.) The probability: P(χ2< 18.307) for df = 10 is ____0.95_________
13. (0.5 pts.) The rejection region for a one-way χ2 test of a null hypothesis p1= p2= . . .= pk if k = 8
and α = 0.05 is:
A. χ2>15.507
B. χ2>14.067
C. χ2<14.067
D. χ2<15.507
14. 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
15. (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
16. (0.5 pts.) In the above hypothesis test, what would be your decision at 0.025 significance
level?
A. Reject the Null (because 8 > 7.378)
B. Fail to reject the Null
C. Not enough information to make a decision
D. Depends on the alternate hypothesis
17. (0.5 pts.) 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.
18. 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 = 0.05.
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_______
19. (0.5 pt.) For the above test of independence, what is the critical value (Use alpha = 0.05)?
3.81
20. (0.5 pt.) What would be your decision in the above hypothesis test at alpha of 0.05?
A. Reject the Null
B. Fail to reject the Null
C. Not enough information to make a decision
D. Depends on the alternate hypothesis
21. (0.5 pt.) Please state your conclusion for the above hypothesis test:
There is enough evidence at significance level of 0.05 that music type and age group are not
independent.