Discussion:
A Managers Dilemma of Buying Smartphones
The procurement manager of a large company was assigned with buying new smartphones for 500 employees. The manager sent out requests for proposals to three companies: AT&B, Horizon and E-Mobile. All three companies responded and the manager saw that he could get the best deal from Horizon. Given that, he completed a purchase order and presented it to the Vice-President of Finance for approval. Despite the good deal he had managed to work out, he was shocked to hear that the Vice-President stated to go with E-Mobile because he said E-Mobile is the industry leader and they always had fewer problems with their equipment than with the smartphones bought from AT&B and Horizon.
The procurement manager, really not believing what he had just heard, went to the director of technical support to look at the maintenance requests for the past five years. He was able to put together a chart showing the actual occurrence of maintenance requests for each of the brands of smartphones. These figures are shown in the chart below. The manager knew that the VP had final authority on the request but wanted to know, for his own peace of mind, if there were really any differences between the amount of maintenance each brand required.
|
Company
|
Total Maintenance Requests
|
|
AT&B
|
25
|
|
Horizon
|
33
|
|
E-Mobile
|
19
|
1. What is the hypothesis that the manager is investigating?
2. What is the independent variable?What are the levels of the independent variable?
3. What is the dependent variable?
4. Which statistical test would he use to test his hypothesis? Is this directional/non-directional chi-square test? Why?
5. For each of the sets of output below, what can you tell about the dependent variable? What decision would the manager make?
Case A
|
Company
|
Observed Number
|
Expected Number
|
Residual
|
|
|
Brand
|
|
AT&B
|
33
|
25.7
|
7.3
|
|
Chi-Square
|
3.844
|
|
Horizon
|
25
|
25.7
|
-0.7
|
|
Degrees of Freedom
|
2
|
|
E-Mobile
|
19
|
25.7
|
-6.7
|
|
p value
|
.146
|
|
Total
|
77
|
|
|
|
|
|
Case B
|
Company
|
Observed Number
|
Expected Number
|
Residual
|
|
|
Brand
|
|
AT&B
|
43
|
25.7
|
17.3
|
|
Chi-Square
|
18.805
|
|
Horizon
|
21
|
25.7
|
-4.7
|
|
Degrees of Freedom
|
2
|
|
E-Mobile
|
13
|
25.7
|
-12.7
|
|
p value
|
.000
|
|
Total
|
77
|
|
|
|
|
|
Case C
|
Company
|
Observed Number
|
Expected Number
|
Residual
|
|
|
Brand
|
|
AT&B
|
15
|
25.7
|
-10.7
|
|
Chi-Square
|
14.442
|
|
Horizon
|
21
|
25.7
|
-4.7
|
|
Degrees of Freedom
|
2
|
|
E-Mobile
|
41
|
25.7
|
15.3
|
|
p value
|
.001
|
|
Total
|
77
|
|
|
|
|
|
Using this chart in each of the three cases find the critical value and describe whether the companies are statistically independent or not.
df 0.995 0.99 0.975 0.95 0.90 0.10 0.05 0.025 0.01 0.005
1 0.001 0.004 0.016 2.706 3.841 5.024 6.635 7.879
2 0.010 0.20 0.051 0.103 1.211 4.605 5.991 7.378 9.210 10.597