CBESTA2 ExercisesAnalysis of Variance

1. The following data represent the number of hours of pain relief provided by 5 different brands of headache tablets administered to 25 subjects. The 25 subjects were randomly divided into 5 groups and each group was treated with a different brand.

TabletA B C D E5 9 3 2 74 7 5 3 68 8 2 4 96 6 3 1 43 9 7 4 7

Total 26 39 20 14 33 132Mean 5.2 7.8 4.0 2.8 6.6 5.28

Perform the analysis of variance, and test the hypothesis at the 0.05 level of significance that the mean number of hours of relief provided by the tablets is the same for all five brands.

2. Six different machines are being considered for use in manufacturing rubber seals. The machines are being compared with respect to tensile strength of the product. A random sample of 4 seals from each machine is used to determine whether the mean tensile strength varies from machine to machine. The following are the tensile strength measurements in kilograms per square centimeter:

Machine1 2 3 4 5 6

17.5 16.4 20.3 14.6 17.5 18.316.9 19.2 15.7 16.7 19.2 16.215.8 17.7 17.8 20.8 16.5 17.518.6 15.4 18.9 18.9 20.5 20.1

Perform the analysis of variance at the 0.05 level of significance and indicate whether or not the mean tensile strengths differ significantly for the 6 machines.

3. To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, the Jacobs Chemical Company obtained the following data on the time (in minutes) needed to mix the material.

Manufacturer1 2 3

20262422

28263127

20192322

a. Use this data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use a 0.05 level of significance.

b. At a 0.05 level of significance, use Fisher’s LSD procedure to test which manufacturers have a significant difference in the mean time for mixing a batch of material.

4. It is suspected that higher priced automobiles are assembled with greater care than lower-priced automobiles. To investigate this, a large luxury model A, a medium size sedan B, and a subcompact hunchback C were compared for defects when they arrived at the dealer’s showroom. All cars were manufactured by the same company. The number of defects for several of the three models were recorded and are shown below:

ModelA B C4 5 87 1 66 3 86 5 9

3 54

Test the hypothesis at the 0.05 level of significance that the average number of defects is the same for the three models.

5. Managers at all levels of an organization need adequate information to perform their respective tasks. One study investigated the effect the source has on the dissemination of information. In this particular study the sources of information were a superior, a peer, and a subordinate. In each case, a measure of dissemination was obtained, with higher values indicating greater dissemination of information. Using a 0.05 level of significance and the following data, test whether the source of information significantly affects dissemination. What is your conclusion and what does it suggest about the use and dissemination of information?

Superior Peer Subordinate

85466755

66753476

65743575

6. A study investigated the perception of corporate ethical values among individuals specializing in marketing. Using a 0.05 level of significance and the following data, (higher scores indicate higher ethical values),

Marketing Managers Marketing Research Advertising

654564

554454

676566

a. Test for significant differences in perception among the three groups of specialists.b. Use Fisher’s LSD to determine where the differences occur.

7. The Texas Transportation Institute at Texas A&M University conducted a survey to determine the number of hours per year drivers waste sitting in traffic. Of 75 urban areas studied, the most jammed urban area was Los Angeles where drivers wasted an average of 90 hours per year. Other jammed urban areas included Denver, Miami, and San Francisco. Assume sample data for six drivers in each of these cities show the following number of hours wasted per year sitting in traffic.

Denver Miami San Francisco706271585766

667055655666

656274696375

a. Using a 0.05 level of significance, test for significant differences among the population mean wasted time for these three urban areas. What is your conclusion?

b. If there is a significant difference between the three cities, determine where the differences occur using Fisher’s LSD procedure.

8. To test for any significant difference in the number of hours between breakdowns for four machines, the following data were obtained:

Machine 1 Machine 2 Machine 3 Machine 46.47.85.37.48.47.3

8.77.49.4

10.19.29.8

11.110.39.7

10.39.28.8

9.912.812.110.811.311.5

a. At a 0.05 level of significance, determine if there is a significant difference between the population times of the four machines.

b. Use Fisher’s LSD procedure to test for the equality of means. Where do the differences occur? Use a 0.05 level of significance.

9. An investigator wants to determine whether there is a significant difference between three different smoking cessation programs in terms of recidivism. He conjures up a study to see how many days a person was smoke-free during the first 30 days. Following are his data:

ProgramA B C30 25 2125 23 2027 20 2225 19 1620 18 1422 14 18

Is there a significant difference between the three programs? Use a 0.05 level of significance.

10. Three varieties of potatoes are being compared for yield. The experiment was conducted using 9 uniform plots at each of 4 different locations. Each variety of potato was planted at each location on 3 plots selected at random. The yields, in 100 kilograms per plot, were as follows:

LocationVariety of Potato

A B C

1151912

202418

221714

2171013

241822

261921

39

126

121510

1058

4148

11

211614

191512

Use a 0.05 level of significance to test the hypothesis thata. there is no difference in the yielding capabilities of the 3 varieties of potatoes;b. different locations have no effect on the yields;c. the locations and varieties of potatoes do not interact.

11. The following are the number of words per minute typed by 4 secretaries on 4 different typewriter models:

SecretaryTypewriter Model

Royal IBM Underwood OlivettiKim 78 62 71 77

Doug 57 49 62 60Rhonda 69 78 72 83Kevin 71 66 59 67

Use a 0.05 level of significance to test the hypothesis thata. the secretaries type with equal speed;b. different typewriters have no effect on typing speed.