Main Module 4
Comparing Multiple Samples of Numerical Data

 

Learning Objectives

At the end of the module, the student will:

  Understand the concept and objective of two-sample tests with numerical data.

Using Microsoft Excel, select, perform and interpret the:

·         Appropriate hypothesis test for the difference between two means based on samples drawn from independent populations.

·         Hypothesis test for the difference between two variances based on samples drawn from independent populations.

·         Hypothesis test for the difference between two means based on samples drawn from related populations.

Understand the concept of and objective of multiple sample tests with numerical data.

Using Microsoft Excel, select, perform and interpret the:

    • Hypothesis test for differences in multiple means in one-way completely randomized ANOVA model.

 

Module Notes

The following sub modules contain summary notes for the six content topic areas of Module 4.

Module 4.1: Comparing Two Independent Samples of Numerical Data

Module 4.2: Comparing Two Related Samples of Numerical Data

Module 4.4: Comparing Multiple Samples of Numerical Data: One Factor

Assignment 4 - Part 1  (see Module 5 for Part 2)

1. Reference the data in the Table of Product Ratings. These are product ratings from randomly selected test market participants using a new product after viewing five different product advertisements. For example, the new product was rated a 15 by the first participant viewing Advertisement A. The rating scale is numeric with a range of 0 to 20, 20 being the most favorable rating.

This exercise requires that you do the Excel analysis. This is good practice and helps prepare you to use this technique in the future.

Using Microsoft Excel for the analysis,

a. Enter the data in a new spreadsheet.

b. Select, perform and interpret the appropriate t-test for the difference between two means. Compare the sample in Column E in the Table of Product Ratings for Five Advertisements against the sample of New Data (from high school students). Hint: run an F-test for differences between two variances to determine which t-test to use. State your conclusion.

c. Perform and interpret the one-way ANOVA for differences in multiple means using the data in the table of Product Ratings for Five Advertisements (exclude New Data from this test).  State your conclusion.

d. If you determine that there is a significant difference in the five means (step c), use the Bonferroni Multiple Comparison Procedure to determine which pairs of means are different.  State your conclusion.

e. Show all your work on a spreadsheet file.

Table of Product Ratings

A

B

C

D

E

New Data

15

16

8

5

12

14

18

17

7

6

19

13

17

20

10

13

18

15

19

16

15

11

12

9

19

19

14

9

17

11

20

18

14

10

14

13

 

 

 

 

 

12

 

 

 

 

 

16

2. The manager of the Tammy Corporation wants to determine whether or not the type of work schedule for her employees has any effect on their productivity.  She has selected 15 production employees at random and then randomly assigned 5 employees to each of the 3 proposed work schedules.  The following table shows the units of production (per week) under each of the work schedules.

Work Schedule (Treatments)

Work Schedule 1

Work Schedule 2

Work Schedule 3

50

60

70

60

65

75

70

66

55

40

54

40

45

57

55

State the hypotheses and determine if there is a significant difference in the mean weekly units of production for the three types of work schedules at  0.05 level of significance.

3. In computing the standard of living index, commuting time represents a heavy weight in determining the desirability of the city or community.  If two cities have the same commuting time to drive to work, then the weight in the index is the same for both cities/communities.  Random samples of commuters are taken from two cities.  The following data represents the time (in minutes) to drive to work.  Use Excel to determine whether the average commuting times are significantly different between the two cities.  Use α = .05.

                          City A                        

City B

15.25

40.25

12.75

48.75

25.50

50.00

12.50

12.25

18.75

45.00

15.50

19.00

60.25

16.75

22.75

42.00

10.50

18.75

38.75

42.50

10.50

28.50

45.00

12.25

35.75

30.00

 

 

4. The daily production rates for a sample of banking processing facility workers before and after a training program are shown below.

Worker

Before

After

1

6

9

2

10

12

3

9

10

4

8

11

5

7

9

At a .05 level of significance, use Excel to test to see if the training program was effective.  That is, did the training program actually increase the production rates?

Practice problems:

You may want to solve these problems related to Module 4 in this link.  The solution is included.

Optional Text Reading

Anderson, D., Sweeney, D., & Williams, T. (2007). Essentials of Modern Business Statistics with Microsoft Excel. Cincinnati, OH: South-Western, Chapter 10 & 11

Lind, D., Marchal, W., and Wathen, S., Statistical Techniques in Business and Economics, 12th edition, McGraw-Hill-Irwin. Chapter 10.

Ken Black. Business Statistics for Contemporary Decision Making. Fourth Edition, Wiley. Chapter 10 & 11

Groebner, D., Shannon, P., Fry, P., and Smith, K. Business Statistics Fifth Edition, Prentice Hall, Chapter 10