Week 5

The following is sample information. Test the hypothesis that the treatment means are equal. Use the 0.05 significance level.

Treatment 1

Treatment 2

Treatment 3

6          

4          

4          

3          

6          

7          

6          

5          

7          

5          

4          

5          

(a)

State the null hypothesis and the alternate hypothesis.

  H₀

  H₁

(b)

What is the decision rule? (Round your answer to 2 decimal places.)

   H₀ if the test statistic is greater than .

(c&d)

Compute SST, SSE, and SS total and complete an ANOVA table. (Round SS, MS and F values to 3 decimal places.)

  Source

SS

df

MS

F

  Treatments

  Error

  Total

(e)

State your decision regarding the null hypothesis.

H₀

A senior accounting major at Midsouth State University has job offers from four CPA firms. To explore the offers further, she asked a sample of recent trainees how many months each worked for the firm before receiving a raise in salary. The sample information is submitted to MINITAB with the following results:

  Analysis of Variance

  Source

DF

SS

MS

F

  Factor

3       

29.81   

9.94   

11.77    

  Error

10       

8.44   

.84   

  Total

13       

38.25   

Reject if F > . (Round your answer to 2 decimal places.)

At the 0.05 level of significance, is there a difference in the mean number of months before a raise was granted among the four CPA firms?

the following data are given for a two-factor ANOVA.

Treatment

Block

1

2

A

46

38

B

32

24

C

47

32

Using the .05 significance level conduct a test of hypothesis to determine whether the block or the treatment means differ.

(a)

State the null and alternate hypotheses for treatments;

  H₀

  H₁

(b)

State the decision rule for treatments. (Round your answer to 1 decimal place.)

   H₀ if the test statistic is greater than .

(c)

State the null and alternate hypotheses for blocks.

  H₀

  H₁

Also, state the decision rule for blocks.

if the test statistic is greater than .

(d&e)

Compute SST, SSB, SS total, and SSE and complete an ANOVA table. (Round SS, MS and F values to 2 decimal places.)

  Source

SS

df

MS

F

  Treatments

  Blocks

  Error

  Total

(f)

Give your decision regarding the two sets of hypotheses.

  Decision: Treatments.  

  Decision: Blocks.

Chapin Manufacturing Company operates 24 hours a day, five days a week. The workers rotate shifts each week. Management is interested in whether there is a difference in the number of units produced when the employees work on various shifts. A sample of five workers is selected and their output recorded on each shift. At the 0.05 significance level, can we conclude there is a difference in the mean production rate by shift or by employee?

Units Produced

  Employee

Day

Afternoon

Night

  Skaff

36

23

31

  Lum

36

23

36

  Clark

24

24

33

  Treece

37

28

28

  Morgan

26

23

26

For treatments: Reject Ho if F > . (Round your answer to 2 decimal places.)

For blocks: Reject Ho if F> . (Round your answer to 2 decimal places.)

Decision by shift: difference in the mean production rate.

Decision by employee: difference in the mean production rate.

7.

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

37

46

59

23

70

45

36

47

47

35

58

53

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

  Error

  Total

(2)

Find the values of mean and standard deviation. (Round the mean and standard deviation values to 3 decimal places.)

  Level

N

Mean

StDev

  Clothes

  Food

  Toys

(3)

Is there a difference in the mean attention span of the children for the various commercials?

  The hypothesis of identical means can definitely be.

  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.

8.

when only two treatments are involved, ANOVA and the Student t test (Chapter 11) result in the same conclusions. Also, . As an example, suppose that 14 randomly selected students were divided into two groups, one consisting of 6 students and the other of 8. One group was taught using a combination of lecture and programmed instruction, the other using a combination of lecture and television. 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. Using analysis of variance techniques, test the null hypothesis, that the two mean test scores are equal.

Lecture and
Programmed
Instruction

Lecture and
Television

11

34

12

23

24

35

22

22

12

25

15

25

27

22

(a-1)

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

  Source

SS

df

MS

F

  Factors

  Error

  Total

(a-2)

Use a level of significance. (Round your answer to 2 decimal places.)

  The test statistic is F

(b)

Using the t test from Chapter 11, compute t. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

  t

(c)

There is in the mean test scores.

9.

the city of Tucson, Arizona, employs people to assess the value of homes for the purpose of establishing real estate tax. The city manager sends each assessor to the same five homes and then compares the results. The information is given below, in thousands of dollars. Can we conclude that there is a difference in the assessors, at α = 0.05?

Assessor

Home

Zawodny

Norman

Cingle

Holiday

A

$59

$52

$47

$43

B

  51

  58

  55

  59

C

  43

  56

  41

  54

D

  76

  67

  62

  63

E

  81

  86

  94

  86

(a)

Is there a difference in the treatment means, at α = .05? (Round your answer to 2 decimal places.)

The computed F value is .

Decision: a difference in the treatment means.

(b)

Is there a difference in the block means, at α = .05? (Round your answer to 2 decimal places.)

The computed F is .

Decision: a difference in the block means.

Three supermarket chains in the Denver area each claim to have the lowest overall prices. As part of an investigative study on supermarket advertising, the Denver Daily News conducted a study. First, a random sample of nine grocery items was selected. Next, the price of each selected item was checked at each of the three chains on the same day. Use 0.05 level of significance.

Item

Super$

Ralph's

Lowblaws

1

$1.12

$1.02

$1.07

2

1.14

1.10

1.21

3

1.72

1.97

2.08

4

2.22

2.09

2.32

5

2.40

2.10

2.30

6

4.04

4.32

4.15

7

5.05

4.95

5.05

8

4.68

4.13

4.67

9

5.52

5.46

5.86

(a-)

Is there a difference in the item means and in the store means?