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QMS 202 (10)
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ch 13 & 14 review questions.pdf

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Department
Quantitative Methods
Course
QMS 202
Professor
Jason Chan
Semester
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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