## Independent variable(s)

Problems — Partial

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)

- 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.

- 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.

- 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.

- 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.

- 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.

- 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

- What is Post-ANOVA test? Why is it necessary? When? Explain with an example.

(4 + 2 + 2 points) - 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