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Statistics : Hypothesis Testing, Significance Levels, ANOVA, Tukey-Kramer, Wilcoxon Rank Sums Test and Kruskal-Wallis Rank Test

1. Which of the following components in an ANOVA table are not
additive?

a. Sum of squares
b. Degrees of freedom
c. Mean squares
d. It is not possible to tell

2. Why would you use the Tukey-Kramer procedure?

a. To test for normality
b. To test for homogeneity of variance
c. To test independence of errors
d. To test for differences in pair wise means

3. A completely randomized design

a. has only one factor with several treatment groups.
b. can have more than one factor, each with several treatment
groups.
c. has one factor and one block.
d. has one factor and one block and multiple values.

4. In a one-way ANOVA, the null hypothesis is always
a. There is no treatment effect.
b. There is some treatment effect.
c. All the population means are different.
d. Some of the population means are different.

5. Interaction in an experimental design can be tested in

a. a completely randomized model.
b. a randomized block model.
c. a two-factor model.
d. all ANOVA models.

6. Suppose there is interest in comparing the median response time for
three independent groups learning a specific task. The appropriate
nonparametric procedure is

a. Wilcoxon Rank Sums Test.
b. Wilcoxon Signed Rank Test.
c. Kruskal-Wallis Rank Test for Differences in Medians.
d. None of the above.

7. A campus researcher wanted to investigate the factors that affect
visitor travel time in a complex, multilevel building on campus.
Specifically, he wanted to determine whether different building
signs (building maps versus wall signage) affect the total amount of
time visitors require to reach their destination and if that time
depends on whether the starting location is inside or outside the
building. Three subjects were assigned to each of the combinations
of signs and starting locations, and travel time in seconds from
beginning to destination was recorded. How should the data be
analyzed?

Starting Room______________________________

Interior Exterior____________

Wall Signs 141, 119, 238 224, 339, 139 224, 339, 139________

Map 85, 94, 126 226, 129, 130_________

a. Completely randomized design
b. Randomized block design
c. 2x2 factorial design
d. Kruskal-Wallis rank test

8. You are working with an experiment that has a single factor of
interest with five groups or levels, and seven observations in each
group. How many degrees of freedom are there in determining the
within-group variation?

a. 4
b. 6
c. 30
d. 34

9. You are working with an experiment that has a single factor of
interest with five groups or levels, and seven observations in each
group. You have calculated SSA = 60 and SST = 210. At
the .05 level of significance, what is the value of the upper-tail
critical value from the F distribution?

a. 2.69
b. 3.00
c. 3.25
d. 5.00

10. Given a randomized block experiment having one factor containing
four treatment levels and 8 blocks, MSA = 80, SSBL = 540, and
F among blocks = 5.0, what is the MSBL (mean square or variance
among blocks)?

a. 15.4286
b. 77.1429
c. 67.5000
d. 16.0000

11. A chef was experiencing difficulty in getting brands of pasta cooked
to the appropriate firmness. She conducted an experiment with two
brands of pasta cooked for either 4 minutes or for 8 minutes. The
response variable measured was the weight of the pasta. The result
(in terms of weight in grams) for two replications of each type of
pasta and cooking time are as follows:

Cooking Time Cooking Time
(minutes) (minutes)_____
Pasta Type 4 8 Pasta Type 4 8__
American 265 310 Italian 250 300

270 320 245 305

At the .05 level of significance, what is the F statistic used to test
whether there is an interaction between the type of pasta and the
cooking time?
a. 1.28571
b. 7.70865
c. 24.1429
d. 28.1250

12. An industrial psychologist wants to test whether the reaction times
of assembly line workers are equivalent under three different
learning methods. From a group of 25 new employees, 9 are
randomly assigned to method A, 8 to method B and 8 to method C.
After the learning period the workers are given a task to complete,
and their reaction times are measured as shown in the table below.
What is the appropriate test statistic to use for measuring whether
there is a significant difference between the median reaction times
for these learning methods at a significance level of 0.01?

METHOD
A B C
2 1 5
3 6 7
4 8 11
9 15 12
10 16 13
14 17 18
19 21 24
20 22 25
23

a. 2 χ = 9.210
b. 2 χ = 5.991
c. H = 0.12
d. H = 0.64

13. Given a randomized block experiment having a single factor of
interest with five treatment levels and seven blocks, with the
following sums of squares already calculated: SSA = 60, SSBL = 75
and SST = 210, form the ANOVA summary table, then answer the
following question. Which of the following most accurately
represents the decision rule for testing the null hypothesis that
there are no block effects at a .05 significance level?

a. If F > 2.51, reject H0
b. If F > 2.78, reject H0
c. If F > 4.00, reject H0
d. If F > 4.80, reject H0

14. If we use the χ2 method of analysis to test for the differences among
4 proportions, the degrees of freedom are equal to:

a. 3
b. 4
c. 5
d. 1

15. If we wish to determine whether there is evidence that the
proportion of successes is the same in Group 1 as in Group 2, the
appropriate test to use is

a. The Z test
b. The χ2 test
c. Both of the above
d. None of the above

16. A study published in the American Journal of Public Health was
conducted to determine whether the use of seat belts in motor
vehicles depends on ethnic status in San Diego County. A sample of
792 children treated for injuries sustained from motor vehicle
accidents was obtained, and each child was classified according to
(1) ethnic status (Hispanic or non-Hispanic) and (2) seat belt usage
(worn or not worn) during the accident. The number of children in
each category is given in the table below.

Hispanic Non-Hispanic
Seat belts worn 31 148
Seat belts not worn 283 330

Using the data from the table above, the calculated test statistic is
a. -0.9991
b. -0.1368
c. 48.1849
d. 72.8063

17. Many companies use well-known celebrities as spokespersons in
their TV advertisements. A study was conducted to determine
whether brand awareness of female TV viewers and the gender of
the spokesperson are independent. Each in a sample of 300 female
TV viewers was asked to identify a product advertised by a celebrity
spokesperson. The gender of the spokesperson and whether or not
the viewer could identify the product was recorded. The numbers in
each category are given below.

Male Celebrity Female Celebrity
Identified product 41 61
Could not identify 109 89

Referring to the table above, at 5% level of significance, the critical
value of the test statistic is
a. 3.8415
b. 5.9914
c. 9.4877
d. 13.2767

18. A computer used by a 24-hour banking service is supposed to
randomly assign each transaction to one of 5 memory locations. A
check at the end of a day's transactions gave the counts shown in
the table to each of the 5 memory locations, along with the number
of reported errors. The bank manager wants to test whether the
proportion of errors in transactions assigned to each of the 5
memory locations differ. Using the data in the table below, the
calculated value of the χ2 test statistic is

Memory Location 1 2 3 4 5
Number of Transactions 82 100 74 92 102

Number of Reported Errors 11 12 6 9 10

a. - 0.1777
b. - 0.0185
c. 1.4999
d. 1.5190

19. The Wall Street Journal recently ran an article indicating
differences in perception of sexual harassment on the job between
men and women. The article claimed that women perceived the
problem to be much more prevalent than did men. One question
asked to both men and women was: "Do you think sexual
harassment is a major problem in the American workplace?" Some
24% of the men compared to 62% of the women responded "Yes."
Suppose that 150 women and 200 men were interviewed. What
conclusion should be reached?

a. Using a 0.01 level of significance, there is sufficient evidence
to conclude that women perceive the problem of sexual
harassment on the job as much more prevalent than do men.

b. There is insufficient evidence to conclude with at least 99%
confidence that women perceive the problem of sexual
harassment on the job as much more prevalent than do men.

c. There is no evidence of a significant difference between the
men and women in their perception.

d. More information is needed to draw any conclusions from the
data set.

20. A powerful women's group has claimed that men and women differ
in attitudes about sexual discrimination. A group of 50 men (Group
1) and 40 women (Group 2) were asked if they thought sexual
discrimination is a problem in the United States. Of those sampled,
11 of the men and 19 of the women did believe that sexual
discrimination is a problem. Which of the following are the
appropriate null and alternative hypotheses to test the group's
claim?
a. H0: M W &#961; &#961; &#8722; &#8805; 0 versus H1: M W &#961; &#961; &#8722; < 0
b. H0: M W &#961; &#961; &#8722; &#8804; 0 versus H1: M W &#961; &#961; &#8722; > 0
c. H0: M W &#961; &#961; &#8722; = 0 versus H1: M W &#961; &#961; &#8722; &#8800; 0
d. H0: M W µ µ &#8722; &#8804; 0 versus H1: M W µ µ &#8722; > 0

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Solution Summary

Hypothesis Testing, Significance Levels, ANOVA, Tukey-Kramer, Wilcoxon Rank Sums Test and Kruskal-Wallis Rank Test are investigated. The solution is detailed and well presented.

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