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Homework answers / question archive / Question1) Cindy Ho, VP of Finance at Discrete Components, Inc

Question1) Cindy Ho, VP of Finance at Discrete Components, Inc

Math

Question1) Cindy Ho, VP of Finance at Discrete Components, Inc. (DCI), theorizes that the discount level offered to credit customers affects the average collection period on credit sales. Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%) by randomly assigning five customers to each sales discount rate. An analysis of Cindy's data produced the following ANOVA table.

 

   
 

 

Source of Variation

SS

df

MS

F

Treatment

1844.2

3

614.7333

7.568277

Error

1299.6

16

81.225

 

Total

3143.8

19

 

 



Based on these results, using a 5% significance level __________

     
       
  • Question 2

0 out of 0.3 points

   
 

BigShots, Inc. is a specialty e-tailer that operates 87 catalog Web sites on the Internet. Kevin Conn, Sales Director, feels that the style (color scheme, graphics, fonts, etc.) of a Web site may affect its sales. He chooses three levels of design style (neon, old world and sophisticated) and randomly assigns six catalog Web sites to each design style. Analysis of Kevin's data yielded the following ANOVA table.

Source of Variation

SS

df

MS

F

Between Groups

1525

     

Within Groups

     

 

Total

3950

 

 

 


What is the observed value of the F statistic for this experiment ? (use two decimals)

     
       
  • Question 3

 

   
 

How do promotions affect product sales ?  As a marketing manager, you assign one of three display types to each of 150 stores and record the change in dollar sales for your product from the previous week.  You want to conduct am ANOVA to find out if all three display types are equally effective.

The number of treatment levels in this experiment is _____

     
       
  • Question 4

 

   
 

While reviewing staffing plans for a new pilot plant, Colin Chenaux, VP of Operations at Clovis Chemicals, Inc., designed an experiment to test the effects of "supervisor's style" and "training method" on the productivity of operators. The treatment levels were: (1) authoritarian, and participatory for supervisor's style, and (2) technical manuals, training films, and multimedia for training method. Three qualified applicants were randomly selected and assigned to each of the six cells. Analysis of Colin's data produced the following ANOVA table.

Source of Variation

SS

df

MS

F

Rows (supervisor's style)

 410.89

1

 

 

Column (training method)

 120.78

2

 

 

Interaction

 2.11

2

 

 

Within

  109.33

12

 

 

Total

 643.11

17

 

 

The value of the mean square error is _____

     
       
  • Question 5

 

   
 

A researcher is studying treatments for agoraphobia with panic disorder. The treatments are to be the drug Imipramine at the following doses: 1.5 mg per kg of body weight, and 2.5 mg per kg of body weight. There will also be a control group given a placebo. Thirty patients were randomly divided into three groups of 10 each. One group was assigned to the control, and the other two groups were assigned to the two treatments. After 24 weeks on treatment, each of the subject's symptoms were evaluated through a battery of psychological tests, where high scores indicate a lessening of symptoms. Assume the data for the three groups are independent, and the data are approximately normal. The means and standard deviations of the test scores for the three groups are given below.

Mean test score

Std. dev. in score

Group

 

 

  75.70000

12.605554

Control

  84.10000

18.441800

Dose = 1.5

102.40000

20.823064

Dose = 2.5


An ANOVA F test was run on the data. Below is a portion of the results.

Source

df

Sums of squares

Mean square

F-ratio

 

Group

 

3727.8

 

 

Error

 

 

310.87

 

 

Total

29

 

 

 


The error degrees of freedom is _____

 

     

 

     
  • Question 6

 

   
 

A tool manufacturer tests three types of cutters used in lathe operations. One type is a laminated steel cutter consisting of a very hard high carbon steel sandwiched between two softer steels. Another is a special high-speed tool steel cutter developed using powder metallurgy. The final one is made from cryogenically treated steel. Several cutters of each type are tested to see how long they will last (in hours) in continuous operation until they need to be sharpened. The times are recorded for each cutter used in the study, and the results are summarized below. n is the number of cutters used of the type indicated.


Assume the data are three independent SRSs, one from each of the three populations of cutters, and that the distribution of the times until sharpening is needed is normal.

A partial ANOVA table is given below.

Source

df

Sums of squares

Mean square

F-ratio

 

Cutter type

 

505.26

 

 

 

 

Error

 

 

 

53.45

 

 

Total

 

 

 

 

 


The total degrees of freedom  is ________

 

     
       
  • Question 7

 

   
 

A milk company has four machines that fill gallon jugs of milk. The quality control manager is interested in determining whether the average fill for these machines is the same.  The following data represent random samples of fill measures (in quarts) for 19 jugs of milk filled by the different machines.  Using a significance level of 1%, develop an ANOVA to determine if the average fill for these machines is the same.

Machine 1

Machine 2

Machine 3

Machine 4

7

11

15

19

8

12

16

20

9

13

17

21

10

14

18

22


The observed value of the F statistic is ____  (use two decimals)

     
       
  • Question 8

 

   
 

Cindy Ho, VP of Finance at Discrete Components, Inc. (DCI), theorizes that the discount level offered to credit customers affects the average collection period on credit sales. Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%). First, she classified DCI's credit customers into three categories by total assets (small, medium, and large). Then, she randomly assigned four customers from each category to a sales discount rate. An analysis of Cindy's data yielded the following ANOVA table.

Source of Variation

SS

df

MS

F

Treatment

64.91667

3

21.63889

8.752809

Block

10.5

2

5.25

2.123596

Error

14.83333

6

2.472222

 

Total

90.25

11

 

 


Using a significance level alpha = 0.05, the appropriate decision for block effects is ________.

 

     
       
  • Question 9

 

   
 

A milk company has four machines that fill gallon jugs of milk. The quality control manager is interested in determining whether the average fill for these machines is the same.  The following data represent random samples of fill measures (in quarts) for 19 jugs of milk filled by the different machines.  Using a significance level of 1%, develop an ANOVA to determine if the average fill for these machines is the same.

Machine 1

Machine 2

Machine 3

Machine 4

7

9

9

10

8

10

9

10

9

11

10

11

10

12

11

12


The p-value for the ANOVA F test is _______ (use two decimals )

 

     
       
  • Question 10

 

   
 

Pate's Pharmacy, Inc. operates a regional chain of 120 pharmacies. Each pharmacy's floor plan includes a greeting card department which is relatively isolated. Sandra Royo, Marketing Manager, feels that the level of lighting in the greeting card department may affect sales in that department. She chooses three levels of lighting (soft, medium, and bright) and randomly assigns six pharmacies to each lighting level. Analysis of Sandra's data yielded the following ANOVA table.

Source of Variation

SS

df

MS

F

Treatment

3608.33

   2

 

 

Error

13591.67

15

 

 

Total

17200

17

 

 


The observed value of the F statistic is _______   (use two decimal places)

 

     
       

 

 

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