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

ECON 2202 –Statistical Methods in Economics and Business II

EXCEL ASSIGNMENT

WINTER 2016

Due: by END OF CLASS (11:30) Thursday April 7, 2016

NO LATE ASSIGNMENTS ARE ACCEPTED.

IT MUST BE SUBMITTED TO COMPLETE THE COURSE REQUIREMENTS

READ ALL INSTRUCTIONS BEFORE BEGINNING!!!!!!!!

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)}= F_0.05,(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 < ? = 0.05

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 significant.

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'S	17.1	12.4
BURGER KING	7.9	7.5
TACO BELL	4.8	6.8
PIZZA HUT	4.7	8.7
WENDY'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