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ECON 2202 – Statistical Methods in Economics and Business II EXCEL ASSIGNMENT WINTER 2016 Late…

ECON 2202 –Statistical Methods in Economics and Business II

EXCEL ASSIGNMENT

WINTER 2016

 

  1. Late assignments receive a grade of 0. Failure to submit this assignment leads to an FND in the course.
  2. You must use EXCEL in the questionswhere indicated for this assignment. Copy and paste the tables into EXCEL from the text below.You must hand in all EXCEL output where indicated. .
  3. The assignment otherwise is hand written. Please label the Excel outputs with the question numbers.
  4. Students may work together on the assignment, but each student MUST submit the assignment independently.
  5. Keep a copy of this assignment to study from, solutions will be posted.
  6. All hypothesis tests MUST use the five steps. Formulae are necessary in all cases unless otherwise noted. For this assignment ONLY you can follow these examples to keep the document smaller and save time!! The conclusions MUST be complete IN CONTEXT as always.

F-test:

1. Ho: regression is not significant, Ha: regression is significant

2. ?=0.05, one-tailed. F?,(k, n-k-1)= F0.05,(2,7)= 6.542

3. Reject Ho if F0 >F?

4. F = MSR/MSE = 43.3648

5. Since F0 > F?(43.3648> 6.542), reject Ho. The regression equation is significant; the relationship between apples and oranges is significant.

OR if using p-values

P-value approach

1. Ho: regression is not significant, Ha: regression is significant

2. ?=0.05, one-tailed

3. Reject Ho if p-value < =="">

4. p-value = 0.0001

5. Since p-value = 0.0001 < =="" 0.05,="" reject="" ho.="" the="" regression="" equation="" is="" significant;="" the="" relationship="" between="" apples="" and="" oranges="" is="">

1. (16 +3 for Excel work) A company is reviewing the performance of two different suppliers of toner ink as their intention is to compare them and possible switch to the alternate one. Using the following data for hours of toner use before empty and alpha = 0.05 in all cases answer the following.

CURRENT SUPPLIER A

ALTERNATE SUPPLIER

B

486

489

490

489

491

491

491

492

494

492

494

492

496

492

498

493

498

493

498

494

502

495

504

496

505

497

506

497

507

497

508

498

510

499

514

502

515

503

527

505

a. (5) Determine if the standard deviation of the Alternate Supplier B is significantly less than 5. Use alpha = 0.05. (No EXCEL)

b. (3) Determine if the variation of the hours of toner use of Current Supplier A is greater than that of Alternate Supplier B. Use EXCEL, include printout of result andDO NOT USE p-values in test write up.

c. (3) Determine if there is any difference in the variation of the hours of toner use between the two suppliers. Use EXCEL, include printout of result andDO NOT USE p-values in test write up.

d. (3) Using the findings of part (c), test to determine if Current Supplier A has higher average hours of toner use than Alternate Supplier B. Use EXCEL, include printout of result and use p-values in test.

e. (2) What is your recommendation to the company with respect to the supplier to select? Explain.

2. (3+1 for Excel work) Public health in a local hospital decided to test whether the length of time that nurses wash their hands will alter the amount of bacteria remaining on them. To ensure consistency in the testing nine nurses were selected and each washed their hands, in the first trial for 2.5 seconds and in the second for 15 seconds. The amount of remaining bacteria was measured in each case. Test the hypothesis that longer washing leads to less bacteria remaining. Use alpha = 0.05.

CULTURE 1

CULTURE 2

66

78

132

115

120

93

187

48

190

77

17

3

33

12

92

12

1000

146

3. (15+1 for Excel work) Grading assignments is a real problem, taking a great deal of time and while many students do a poor job, many copy and gain no benefit. An instructor who taught three sections of a course carried out a test. One section had no assignments, one had assignments but they were not graded, and the final section had graded assignments. Grades were reviewed after the first midterm. Assume each population is normally distributed, and samples are independent random samples. Using EXCEL where possible performALL ANOVA tests necessary to determine which approach if any led to higher grades. Use alpha = 0.05 in all tests. Use EXCEL for the ANOVA test and use the p values in testing. For those tests for which you cannot use EXCEL, use the standard write up as used in the practice assignments.

No Assignments

Assignments, Not Graded

Assignments, Graded

69

73

83

69

63

97

92

68

72

84

79

79

79

57

84

84

68

76

76

72

91

63

74

76

76

49

83

82

84

88

89

79

91

72

71

96

72

80

68

65

74

99

73

71

89

47

63

80

92

88

79

71

83

91

83

89

83

81

82

83

92

69

76

80

92

90

64

79

79

72

81

67

84

76

86

79

81

86

74

81

82

81

75

84

4. (9+1 for Excel work) The instructor in the previous example teaches the same sections of the course four times a year and wanted to investigate if there was not only a difference in the way assignments were treated but also in the time of year the course was given. The following data was collected. Assume all populations are normally distributed, observations are independent, and population variances are equal. Using EXCEL perform all remaining tests necessary to determine whether the grades were influenced by assignment method and/or semester. Use alpha = 0.05 in all tests. No post tests are required.

TERM

No Assignments

Assignments, Not Collected

Assignments, Collected

FALL

69

73

83

69

63

97

92

68

72

84

79

79

79

57

84

84

68

76

76

72

91

WINTER

63

74

76

76

49

83

82

84

88

89

79

91

72

71

96

72

80

68

65

74

99

EARLY SUMMER

73

71

89

47

63

80

92

88

79

71

83

91

83

89

83

81

82

83

92

69

76

LATE SUMMER

80

92

90

64

79

79

72

81

67

84

76

86

79

81

86

74

81

82

81

75

84

5. (16) Is the type of beverage ordered with lunch at a restaurant independent of the age of the customer? A random sample of 309 lunch customers was taken and the results are as follows. Using alpha = 0.01, test to determine if the two factors are related. Please show intermediate calculation steps for part marks. (No Excel in this question.)

AGE

COFFEE/TEA

SOFT DRINK

OTHER

21-34

26

95

18

139

35-55

41

40

20

101

OVER 55

24

13

32

69

91

148

70

309

6. (13 +5 for Excel work) Can sales of major fast food chains be explained by the number of individual locations the chain has? Consider the following data where sales are measured in $ billions and locations are in thousands.

SALES

LOCATIONS

MCDONALD&#39;S

17.1

12.4

BURGER KING

7.9

7.5

TACO BELL

4.8

6.8

PIZZA HUT

4.7

8.7

WENDY&#39;S

4.6

4.6

KFC

4

5.1

SUBWAY

2.9

11.2

DAIRY QUEEN

2.7

5.1

A & W

2.7

2.9

Use EXCEL, to create a scatter diagram, correlation matrix, and regression model. Conduct all tests at the 5% significance level.

a) (2) Reviewing the data and the scatter diagram, does the correlation matrix result support the relationship you would expect? Are there any other considerations or concerns that arise from this?

b) (5) Conduct a test to determine whether the population correlation coefficient is significantly different from zero. Do not use p values.

c) (4) Is there an observation which is impacting the relationship?Given your findings in parts (a) and (b), explain what you might consider doing to further investigate this relationship? Rerun the correlation matrix and the equation and compare the two models with respect to the correlation of the variables, the fit (R2), and the significance of the slope. You do not need to write out the tests just use the p values to explain what happens and why when comparing the significance of the model or slope.

d) (2) Which model would you select to examine the relationship? Explain your choice.

7. (15+2 for Excel work) Consider the following data for the average cost of various fuels and electricity for a twelve year period. The data measure the following:

Electricity

Residential rate per kilowatt hour

Natural Gas

Residential natural gas per 1000 cubic feet

Fuel Oil

Residential fuel oil per gallon

Gasoline

Regular gasoline per gallon

Your model will attempt to predict residential electricity costs using the cost of the other fuels.

a) (1) State whether you would expect a positive or negative relationship between electricity costs and each of the independent variables and explain why.

b) (2) Use EXCEL, to create a correlation usingall independent variables provided. Discuss all aspects of the correlation matrix, as it compares to your expectations in part (a) and what it tells you about the potential results of a regression analysis.

c) (3) Use EXCEL to run a multiple regression to estimate electricity costs usingall independent variables provided. Test if the overall regression is significant at the 5% level.

d) (3) Test for the significance of each slope coefficient at the 5% level. (Incorporate all tests into ONE five step answer as in the slides.)

e) (2) Based on your correlation matrix and the results of your regression do you suspect multicollinearity? If yes, which independent variable(s) to you think could be responsible?

f) (2) Explain how you test for multicollinearity but do not test.

g) (2)How could you rerun the regression taking into account the issues in the first regression? Which variable or variables would you keep as an explanatory variable(s), and why?

Electricity

Natural Gas

Gasoline

Fuel Oil

2.54

1.29

0.39

0.21

3.51

1.71

0.57

0.31

4.64

2.98

0.86

0.44

5.36

3.68

1.19

0.61

6.2

4.29

1.31

0.76

6.86

5.17

1.22

0.68

7.18

6.06

1.16

0.65

7.54

6.12

1.13

0.69

7.79

6.12

1.12

0.61

7.41

5.83

0.86

0.34

7.41

5.54

0.9

0.42

7.49

4.49

0.9

0.33

 

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