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Quantitative Methods
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QMS 202
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Quantitative Methods

QMS 202

Jason Chan

Winter

Description

Question#1
The training director of a manufacturing company wants to compare three
different team-based approaches. Each member of a group of 29 new employees
is randomly assigned to one of three team-based methods. After completing
training, the employees in the study are evaluated on the time it takes (in
minutes) to assemble the product. The results are shown in the following table.
Methods Time To Assemble Product
A 8.57, 8.50 , 9.11 , 8.20 , 8.32 , 7.88 , 9.90 , 9.43 , 8.75
B 7.98 , 8.40 , 8.84 , 7.75 , 8.20 , 7.95 , 8.21 , 6.65 , 7.44 , 8.33
C 8.70 , 8.82, 9.26, 8.96 , 8.65 , 8.30, 9.46 , 9.43 , 9.26 , 9.02
At the 0.05 level of significance, is there evidence of a significant difference in the
average assembly time among the team-based methods?
a. What type of parameter(s) is being tested here? (Circle one)
2
x s s ˆ p pˆ t z F
b. Define the parameters associated with the test {include the appropriate
symbol(s)}
c. State the hypothesis using statistical symbols.
Null Hypothesis: _____________________________
Alternative Hypothesis: _____________________________
d. What procedure is used to perform this test? (Circle one)
t test z test ANOVA Chi-Square
e. What condition(s) is/are required for this procedure to be legitimate?
1f. Which specific standardized test statistic is used to test this hypothesis?
Indicate the degree of freedom (df) if appropriate.
z
z df _____________
t df _____________
t df _____________ df ____________
F df _____________
F df _____________ df ____________
2
df _____________
2
df _____________ df ____________
g. What is the value of the test statistic? ________________
h. What is the critical value(s) for t______________
i. What is the p-value for this________________
j. Construct a graph of the most appropriate distribution clearly showing the
critical value(s), test statistic value, and the rejection region
2k. What is the statistical decision and why?
RejectH A Do not rejecHA RejectH0 Do not rejeHt0
because the p-value is
than /2 than /2 to /2 than
than to than2 than 2
to 2
l. In non-technical terms what is your conclusion for this test?
m. Name the procedure which must be carried out in order to complete the test.
State the reason why that procedure can be used.
3Question#2
A nationwide market research study is undertaken to determine the preferences
of various age groups of Canadians for different team sports. A random sample
of 1000 Canadians is selected, and each individual is asked to indicate his/her
favorite team sport. The results are as follows:
Sport
Age Group Baseball Soccer Basketball Hockey
Under 20 26 36 41 47 150
20 and under 30 38 48 80 84 250
30 and under 40 72 22 38 68 200
40 and under 50 96 26 30 48 200
50 and above 134 4 18 44 200
Total 366 136 207 291 1000
At 0.01 level of significance, is there evidence of a significance relationship
between age groups and their preferences in sports?
a. State the hypothesis using statistical symbols.
Null Hypothesis: __________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
Alternative Hypothesis: _____________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
b. What procedure is used to perform this test? (Circle one)
t test z test ANOVA Chi-Square
4c. What condition(s) are required for this procedure to be legitimate? Are the
condition(s) met? Show your work to justify your answer.
d. Which specific standardized test statistic is used to test this hypothesis?
Indicate the degree of freedom (df) if appropriate.
z
z df _____________
t df _____________
t df _____________ df ____________
F df _____________
F df _____________ df ____________
2 df _____________
2
df _____________ df ____________
e. What is the value of the test statistic? ________________
f. What is the critical value(s) for ______________
g. What is the p-value for this ________________
5h. Construct a graph of the most appropriate distribution clearly showing the
critical value(s), test statistic value, and the rejection region
i. What is the statistical decision and why?
RejectH A Do not rejecHA RejectH0 Do not rejeHt0
because the p-value is
than /2 than /2 to /2 than
than to than2 than 2
to 2
j. In non-technical terms what is your conclusion for this test?
6Question#3
The human resources decided to investigate employee perception of the fairness
of two performance evaluation methods. To test the differences between the two
methods, 320 employees were randomly assigned to be evaluated by one of the
methods: 156 were assigned to method 1, where individuals provided feedback
to supervisory queries as part of the evaluation process; 164 were assigned to
method 2, where individuals provided self-assessments of their work
performances. Following the evaluations, employees were asked whether they
considered the performance evaluation fair or unfair. The results are summarize
in the following table:
Evaluation Method
Employee perception 1 2 Total
Fair 126 98 224
Unfair 30 66 96
Total 156 164 320
Using a 0.05 level of significance, is there evidence of a significant difference
between the two methods i

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