For the next four problems just do the following:
(Answer any three of the four questions. If you answer a fourth question and identify that as an extra-credit question, it will be graded for four extra credit points)
A. Identify the independent variable(s) – if any (and define them precisely and indicate they are qualitative or quantitative)
B. Identify the dependent variable – if any (and define them precisely and indicate they are qualitative or quantitative)
C. Identify the type of analysis that is appropriate (Chi-Square test of independence, ANOVA, Regression, or Correlation)
D. Justify why the analysis you identified in part C is correct.
(3 + 3 + 3 + 3 points)
1. Your firm is having quality problem with the production of plastic automotive parts: there are too many defectives. One of your engineers thinks that it’s because the temperature of the process is not controlled carefully enough. Another engineer is sure that it’s because the assembly line is being shut down too often for unrelated reasons. You have decided to analyze the problem and have come up with figures for the percent defective each day recently, the standard deviation of temperature measured hourly each day (as a measure of temperature control), and the number of assembly line stoppages each day. You are interested in finding out which engineer is right.
A.
B.
C.
D.
2. Some critics of big business argue that CEOs are overpaid and that their compensation is not related the performance of their company. To test this theory, data on executive’s total pay and company’s performance was collected from a randomly selected set of fifty companies.
A.
B.
C.
D.
3. Many companies use well-known celebrities in their ads, while other companies create their own spokespersons (such as Maytag repairman). A marketing researcher is interested in investigating the relationship between gender of the spokesperson and brand awareness. Three hundred television viewers were asked to identify the products advertised by celebrity spokespersons.
A.
B.
C.
D.
4. To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, Jacob’s Chemical Company obtained the data on the mixing times from ten batches for each of the machines. What can we conclude?
A.
B.
C.
D.
Problems — Full
For the next two problems just do the following:
A. Set up the appropriate hypotheses (in plain English)
B. Draw appropriate statistical conclusions (based on the printout provided). In your conclusions, make sure to indicate what values you specifically used from the printout (i.e., highlight/mark/circle the relevant values you need from the printout and then use them in your discussion/conclusions).
C. Present proper conclusions for the business problem.
5. As a consulting industrial engineer you are hired to perform a “human factors experiment” at Burstinter & Lobel, a large law firm. A pool of 30 typists of similar ability and experience is selected to participate. Groups of 10 typists each are randomly assigned to one of three working conditions—very noisy atmosphere (90 Db constant), somewhat noisy atmosphere (65 Db constant), and pleasant atmosphere (40 Db constant). The subjects are then asked to type a technical manuscript. The following data represent the number of mistakes on the manuscript make by the typists under the various working conditions.
Groups
Very Noisy
(90 Db) Somewhat Noisy
(65 Db) Pleasant
(40 Db)
14
12
13
13
16
18
19
11
10
13 2
5
8
5
7
6
9
4
10
9 2
6
6
2
4
3
2
1
7
5
At the .01 level of significance, is there evidence of a difference in the average number of errors between the three groups?
(3 + 8 + 6 points)
Please refer to Printout #1 for this problem
A. H0:
H1:
B.
C.
6. A list of best selling cars for 1987 is shown in the table. The 1988 suggested retail price and the total number sold are given in the table below..
MODEL 1988 Price
(in thousands) Number sold
(in thousands)
Hyundai
Oldsmobile Cierra
Nissan Sentra
Ford Tempo
Chev. Corsica
Pontiac Grand Am
Toyota Camry
Chev. Caprice 5.4
11.4
6.4
9.1
10.0
10.3
11.2
12.5 264
245
236
219
214
211
187
177
At = .05, is there evidence of relationship between the two variables?
(3 + 8 + 6 points)
Please refer to Printout #2 for this problem
A H0:
H1:
B.
C.
Essay Questions
7. What is Post-ANOVA test? Why is it necessary? When? Explain with an example.
(4 + 2 + 2 points)
8. The heights of a sample of husbands and wives in the Heightlands are given below. Write down an equation (i.e., the regression equation) predicting the height of a husband (Y) from the height of his wife (X). What is the correlation coefficient for this equation? (2 + 2 points)
Height of husband Height of wife
72 67
68 63
63 58
59 54
___________________________________________________________
Printout #1
One-way ANOVA: Mistakes versus NoiseLevel
Method
Null hypothesis All means are equal
Alternative hypothesis Not all means are equal
Significance level α = 0.05
Equal variances were assumed for the analysis.
Factor Information
Factor Levels Values
NoiseLevel 3 1, 2, 3
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
NoiseLevel 2 546.9 273.433 42.19 0.000
Error 27 175.0 6.481
Total 29 721.9
Model Summary
S R-sq R-sq(adj) R-sq(pred)
2.54588 75.76% 73.96% 70.07%
Means
NoiseLevel N Mean StDev 95% CI
1 10 13.900 2.923 (12.248, 15.552)
2 10 6.500 2.550 (4.848, 8.152)
3 10 3.800 2.098 (2.148, 5.452)
Pooled StDev = 2.54588
Printout #2
Regression Analysis: Number versus Price
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 3311 3310.9 7.77 0.032
Price 1 3311 3310.9 7.77 0.032
Error 6 2556 426.0
Total 7 5867
Model Summary
S R-sq R-sq(adj) R-sq(pred)
20.6396 56.43% 49.17% 23.44%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 302.9 30.9 9.80 0.000
Price -8.78 3.15 -2.79 0.032 1.00
Regression Equation
Number = 302.9 – 8.78 Price
Fits and Diagnostics for Unusual Observations
Obs Number Fit Resid Std
Resid
2 245.0 202.8 42.2 2.30 R
R Large residual