Question

Use the data below for this problem, follow instructions to find answers:

1.64 1.55 1.83 1.94

1.86 1.56 1.56 1.96

1.88 1.92 1.67 1.97

1.69 1.71 1.58 1.99

1.77 1.70 1.84 2.10

1.69 1.59 1.67 1.97

1.58 1.58 1.79 1.88

1.58 1.51 1.61 1.91

1.70 1.68 1.91 2.21

1.71 1.63 1.68 2.01

1.68 1.59 1.76 1.99

1.64 1.83 1.64 1.94

1.68 1.76 1.67 1.98

1.65 1.95 1.76 2.35

1.47 1.61 1.61 1.91

1.80 1.73 1.59 2.10

1.75 1.70 1.65 2.10

1.48 1.63 1.34 1.64

1.59 1.57 1.71 1.89

1.96 1.69 1.75 2.09

2.01 1.57 1.80 2.10

1.67 1.57 1.93 1.97

1.87 1.52 1.77 1.92

2.01 1.61 1.70 2.00

1.59 1.61 1.59 1.89

1.91 1.59 1.61 1.99

1.72 1.77 1.59 1.89

1.51 1.46 1.76 1.81

1.78 1.48 1.79 1.88

1.80 1.54 1.54 1.84

1.93 1.46 1.86 2.23

1.71 1.78 1.56 2.18

1.61 1.70 1.45 1.75

1.70 1.71 1.45 2.00

1.79 1.58 1.79 1.98

1.81 1.65 1.72 2.02

1.92 1.69 1.68 2.22

CASE ASSIGNMENT #2

Please be sure to read the case description for each problem before you begin the case

assignment. By so doing, you will have a clearer understanding of the purpose of the exercise

and how you will conduct the analysis. This could help reduce the amount of time you spend in

the computer lab on this assignment.

Answer the questions listed in this handout.

Currentprices.com keeps a record of the sales prices of gasoline ($/ gallon, at pump) at different

retailing pumps/ locations. The data on regular unleaded gasoline, as recorded at 37 different

pumps at 4 different locations, viz., Allen, Blaze, Corlis, and Dustin. The data is presented in the

spreadsheet entitled

Assgt#2.xls

.

You have to: (1) Analyze the data for the existence of any difference between the true mean

prices at the four different locations using the ANOVA procedure; (2) conduct Tukey’s multiple

comparison procedure on the data; (3) construct individual 95% confidence intervals for the

mean price of regular gasoline in the four locations; and (4) construct a family of simultaneous

95% confidence intervals for the six possible pairwise differences between the mean prices in the

four locations. The general procedure is outlined below.

1. Open the file Assgt#2.xls.

2. Insert a row (under Edit menu) at the top of the spreadsheet then label the columns A, B, C,

and D appropriately. (Allen, Blaze, Corlis, and Dustin, for example)

3. To conduct the ANOVA, select

Data > Data Analysis > Anova: Single Factor > Input

Range = A1:D38, Labels in First Row = check > OK

. The output will appear on a new

worksheet.

4. To continue the analysis with pairwise comparisons, transfer the data to Minitab. Minitab is a

statistical package, currently installed in the College of Business Computer lab. You can stop by

the physical computer lab on the 1

st

floor of BLB or access it in the virtual lab via VMWare.

Visit the web site http://www.cob.unt.edu/lab/virtuallab.php for instructions on how to access the

virtual lab from home, using your PC or Mac. Once in the COB computer lab, select the

Coba

Menu > DSCI > Minitab

, or

COB Menu (Star Icon) > Statistics> Minitab

. Copy the data in the

four columns in Excel (A1:D38), and paste it in Minitab’s top left cell (the gray cell that holds

the header for column C1).

5. Select

Stat > ANOVA > One Way > Response data are in a separate column for each

factor level > Responses = Allen Blaze Corlis Dustin

.

Select the

Comparisons

button. Then select

Tukey = check

and

Tests = check, > OK > OK

.

ANOVA output will appear in Minitab’s Session window. The output includes an ANOVA table

just like the one you got in Excel. Also included is a list of the four locations with corresponding

95% Confidence Intervals for the mean gasoline prices.

The output continues with information on Tukey pairwise comparisons. At the top, grouping

information is presented. Locations that share the same group code (e.g. A, B, etc.) are grouped

together, i.e., do not have significantly different mean gasoline prices. At the bottom of the

pairwise comparisons output, point estimates and confidence intervals for mean price differences

between the 6 possible location pairs are presented. Point estimates that are positive signify that

the location that gets subtracted in the difference has a smaller mean gasoline price, and vice

versa. Intervals that include 0 signify pairs of locations where the mean gasoline prices are not

significantly different.

1) What is the lower limit of the 95% confidence interval for the difference in true mean gasoline prices in Dustin and Blaze?

a) 1.78
b) 1.69
c) 0.346
d) 0.41
e) 0.29

2) What is the best estimate for the true mean price of gas in Blaze?

a) $0.00
b) $1.99
c) $1.64
d) $1.73
e) $1.68

3) The decision, conclusion, and reason for the conclusion of the test of the difference in gasoline prices using ANOVA is:

F.T.R. Ho, conclude there is evidence of gasoline price differences because F calculated is < F critical
F.T.R. Ho, conclude there is no evidence of gasoline price difference because F calculated is < F critical
Reject Ho, conclude there is no evidence of gasoline price differences because F calculated is > F critical
Reject Ho, conclude there is evidence of gasoline price difference because F calculated is > F critical
Reject Ho, conclude there is evidence of gasoline price differences because p value is > F critical

4) What is the calculated value of the test statistic for testing the equality of gas prices in the four counties (overall)?

a. 2.67
b. 0.017
c. 0.05
d. 52.13
e. 2.49

5) What is the estimate of the pooled variance (of error) for the above model of gas prices?

a. 2.49
b. 0.05
c. 52.13
d. 2.67
e. 0.017

Answer 1

(1) answer is e) 0.29

with 95% confidence the margin of error for the difference of Dustin and Blaze=sqrt(2*MSE/r)*t(alpha/2,error df)=

=sqrt(2*0.0173/37)*1.98=0.06

difference of Dustin and Blaze mean prices=1.99-1.64=0.35

lower limit=0.35-0.06=0.29

(2) c) $1.64

the sample mean will be best estimate and its value=1.64

(3)Reject Ho, conclude there is evidence of gasoline price difference because F calculated is > F critical

F calculated(52.13) is > F critical(2.67)

(4) d. 52.13

(5)e. 0.017

Mean square error will be the estimate of pooled variance

the mean and variance are given

Groups	Average	Variance
Allen	1.73	0.0199
Blaze	1.64	0.0132
Corlis	1.68	0.0168
Dustin	1.99	0.0194

following anova information has been generated

ANOVA
Source of Variation	SS	df	MS	F
Between Groups	2.706997	3	0.902332	52.13531
Within Groups (error)	2.492281	144	0.017308
Total	5.199278	147