Statistics Assignment

4)       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

5       

36.39   

7.28   

1.92    

  Error

12       

45.54   

3.80   

  Total

17       

81.93   

Reject if F >

5)       The following data are given for a two-factor ANOVA.

Treatment

Block

1

2

A

43

36

B

37

23

C

42

37

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

  H₁

Also, state the decision rule for blocks.

if the test statistic is greater than  

  Decision: Blocks.

6)       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 0.01 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

35

22

31

  Lum

36

26

34

  Clark

23

27

35

  Treece

32

21

27

  Morgan

21

24

24

For treatments: Reject Ho if F >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

27

44

61

22

49

64

46

37

57

35

56

48

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 isin the mean attention span.

(4)

Are there significant differences between pairs of means?

  Clothes have a mean attention span of at least ten minutesthe 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

14

33

12

21

26

34

25

20

16

29

14

28

21

22

(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.

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

$53

$55

$48

$43

B

  50

  54

  54

  56

C

  45

  58

  42

  57

D

  76

  63

  61

  61

E

  83

  81

  93

  85

(a)

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

The computed F value is 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 Fis a difference in the block means.

10)   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 0.01 level of significance.

Item

Super$

Ralph's

Lowblaws

1

$2.30

$1.23

$1.24

2

2.30

1.70

1.78

3

2.40

3.20

3.10

4

2.40

1.78

1.87

5

1.32

1.47

1.32

6

4.01

3.06

1.82

7

4.31

3.53

2.21

8

4.13

3.07

2.35

9

5.02

4.17

4.21

4)       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

5       

36.39   

7.28   

1.92    

  Error

12       

45.54   

3.80   

  Total

17       

81.93   

Reject if F >

5)       The following data are given for a two-factor ANOVA.

Treatment

Block

1

2

A

43

36

B

37

23

C

42

37

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

  H₁

Also, state the decision rule for blocks.

if the test statistic is greater than  

  Decision: Blocks.

6)       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 0.01 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

35

22

31

  Lum

36

26

34

  Clark

23

27

35

  Treece

32

21

27

  Morgan

21

24

24

For treatments: Reject Ho if F >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

27

44

61

22

49

64

46

37

57

35

56

48

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 isin the mean attention span.

(4)

Are there significant differences between pairs of means?

  Clothes have a mean attention span of at least ten minutesthe 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

14

33

12

21

26

34

25

20

16

29

14

28

21

22

(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.

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

$53

$55

$48

$43

B

  50

  54

  54

  56

C

  45

  58

  42

  57

D

  76

  63

  61

  61

E

  83

  81

  93

  85

(a)

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

The computed F value is 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 Fis a difference in the block means.

10)   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 0.01 level of significance.

Item

Super$

Ralph's

Lowblaws

1

$2.30

$1.23

$1.24

2

2.30

1.70

1.78

3

2.40

3.20

3.10

4

2.40

1.78

1.87

5

1.32

1.47

1.32

6

4.01

3.06

1.82

7

4.31

3.53

2.21

8

4.13

3.07

2.35

9

5.02

4.17

4.21