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Virginia Commonwealth University Probability Statistics Questions
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Mathematics
Virginia Commonwealth University
Description
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9- 2 points
Completely interpret the SPSS output below from a study of the time it takes rats to run
through a maze to get a piece of cheese behind a Black, Red, or Green door at the
end. [Hint: begin your answer with “We are ___% confident that…”, with the
appropriate value in the blank and the remaining details added afterwards.]
10 – points
Dean wishes to determine if the mean cost of new Chevrolet vehicles is the same for the
five Chevrolet dealerships in his city. The same seven vehicles (year, make, and model)
were priced at the five dealerships. Why is it important to treat the vehicles as blocks in
this scenario?
11-6 points
Consider the following partial RBD ANOVA table. Complete the accompanying
partial One-Way ANOVA table for the same study if it were decided that blocks
should not be used.
RBD ANALYSIS OF VARIANCE
Sum of
Source
DF
Squares
Dealership
4
2.9483
Vehicle (Blocks)
6
247.3979
Error
24
1.7322
Total
34
252.0784
Source
ONE-WAY ANALYSIS OF VARIANCE
Sum of
DF
Squares
Dealership
_____
__________
Error
_____
__________
Total
_____
__________
[DF for Dealership =Question Blank][DF for Error =Question Blank][DF for Total
=Question Blank][SS for Dealership =Question Blank][SS for Error =Question
Blank][SS for Total =Question Blank]
13- (10 points)
A psychologist believes that the frequency that a person engages in sexual activity
depends upon what type of relationship that person may be in. She sampled 1772
randomly selected adults and asked them what type of relationship they were in and
how often per week they engaged in sexual activity. Do the data support her
hypothesis? Use the SPSS output below to perform the appropriate six-step test at the
5% significance level using the P-value approach.
14- 15 points
The U.S. Bureau of Prisons publishes data in Statistical Report on the times served by
prisoners released from federal institutions for the first time. Independent random
samples of released prisoners for five different offense categories yielded the following
information on time served, in months.
Offense
Counterfeiting
Drug Laws
Firearms
Forgery
Fraud
ni
13
13
13
13
13
x̄ i
14.5
18.4
18.2
15.6
11.5
si
4.5
3.8
4.5
3.6
4.7
Part a: (9 points)
Do the data provide sufficient evidence at the 1% significance level to conclude that a
difference exists in mean time served by prisoners among the five offense
groups? Show all steps of the appropriate test procedure. Be sure to list any
assumptions that are assumed to be true (do not create any plots).
Part b: (4 points)
Use Tukey-Kramer (Tukey’s W) to determine any differences in the mean time served
by prisoners among the five offense groups (be sure to include an underline
graphic and sentence), or explain why you don’t think there is a difference in the mean
time served by prisoners among the five offense groups.
Part c: (2 points)
Which offense group(s) do you think yield the shortest mean time served? Be sure to
include information from your analysis above as the basis for your answer.
Upload a single PDF of your complete solution (all 3 parts) to this By-Hand exercise in
the box below.
15- 10 points
(By-Hand) The following SPSS output is for an experiment to measure how the quality
of steel, measured by ELAST, an index of quality, is affected by two aspects of a
processing procedure:
CLEAN: concentration of a cleaning agent, and
TEMPR: an index of temperature and pressure.
Perform only appropriate ANOVA and multiple comparison analyses for this Two-way
ANOVA experiment. Please use a 5% significance level (α = 0.05).
6Suppose you have a One-way ANOVA experiment with 7 treatments and 16
observations per treatment, and you fail to reject the null hypothesis. How many
pairwise comparisons will you make?
7
16
21
112
None are needed.
7-
In a Two-way ANOVA experiment with 4 levels of Factor A, 3 levels of Factor B,
and m = 3 observations per treatment combination, the degrees of freedom for
the A*B interaction term is...
3
4
6
112
not defined
ONE-WAY ANALYSIS OF VARIANCE
Source
DF
Sum of Squares
Dealership
4
2.9483
Error
30
249.1301
Total
34
252.0784
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