chapter 12

When only two treatments are involved, ANOVA and the Student’s t test (Chapter 11) result in the same conclusions. Also, As an example, 14 randomly selected Introduction to History students were divided into two groups, one consisting of 6 students and the other of 8. One group took the course in the normal lecture format. The other group of 8 students took the course via the Internet. At the end of the course, each group was given a 50-item test. The following is a list of the number correct for each of the two groups.

Traditional Lecture

Internet

13

35

15

26

25

38

23

26

12

24

14

25

27

25

a-1.

Complete the ANOVA table. (Round SS, MS and F values to 2 decimal places.)

  Source

SS

df

MS

F

  Factors

 in the mean test scores.

The postal service sorts mail as Priority Mail Express, Priority Mail, First-Class Mail, or Standard Mail. Over a period of 3 weeks, 24 of each type were mailed from the Network Distribution Center in Altanta, Georgia, to Des Moines, Iowa. The total delivery time in days was recorded. Minitab was used to perform the ANOVA. The results follow:

  Source

DF

SS

MS

F

P

  Factor

3    

12.64    

4.21    

3.31    

.024    

  Error

92    

116.73    

1.27    

  Total

95    

129.37    

Requirement 2:

What is the decision rule? Use the 0.05 significance level. (Round your answer to 4 decimal places.)

  Reject H₀ if F>

 a difference in the treatment means.

b.

Is there a difference in the block means? (Round your answer to 2 decimal places.)

The computed F is  a difference in the block means.

Martin Motors has in stock three cars of the same make and model. The Sales Manager would like to compare the gas consumption of the three cars (labeled car A, car B, and car C) using four different types of gasoline. For each trial, a gallon of gasoline was added to an empty tank, and the car was driven until it ran out of gas. The following table shows the number of miles driven in each trial.

Distance (miles)

  Types of Gasoline

Car A

Car B

Car C

  Regular

22.4

20.8

21.5

  Super regular

17.0

19.4

20.7

  Unleaded

19.2

20.2

21.2

  Premium unleaded

20.3

18.6

20.4

At 0.05 significance level, state the decision rule for both treatments (Cars) and blocks (Gasoline). (Round your answers to 2 decimal places.)

  For Treatments (cars) reject H₀ if F >

A study of the effect of television commercials on 12-year-old children measured their attention span, in seconds. The commercials were for clothes, food, and toys.

Clothes

Food

Toys

20

33

55

24

43

53

35

34

40

35

50

44

28

47

63

31

42

53

17

34

48

31

43

58

20

57

47

47

51

44

51

54

1.

Complete the ANOVA table. Use .05 significance level. (Round the SS and MS values to 1 decimal place and F value to 2 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

  Source

df

SS

MS

F

p

  Factors

.

  There is in the mean attention span.

4.

Are there significant differences between pairs of means?

  Clothes have a mean attention span of at least ten minutes the other groups.