Homework SourseTwo Computer makers A and B compete for a certain market The
Two Computer makers, A and B, compete for a certain market. Their users rank the quality of computers on a 4-point scale. Is there a significant difference in the customer satisfaction of the computers produced by A and B? (See image below)
Computer \"Not \"Good \"Excellent maker satisfied\" sfied\"Good quality quality 20 10 40 30 70 40 20 20Solution
Null hypothesis: There is no difference between A and B in customer satisfaction
Alternate hypothesis: There is difference between A and B in customer satisfaction
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
not satisfied
satisfied
Good satisfied
excellent satisfied
Total
fo-fe
A
20
40
70
20
150
2
-2
4
-4
B
10
30
40
20
100
-2
2
-4
4
Total
30
70
110
40
250
Expected Frequencies
Column variable
Row variable
not satisfied
satisfied
Good satisfied
excellent satisfied
Total
(fo-fe)^2/fe
A
18
42
66
24
150
0.2222
0.0952
0.2424
0.6667
B
12
28
44
16
100
0.3333
0.1429
0.3636
1.0000
Total
30
70
110
40
250
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
4
Degrees of Freedom
3
Results
Critical Value
7.815
Chi-Square Test Statistic
3.066
p-Value
0.382
Do not reject the null hypothesis
Calculated chi square value 3.066 < table value of chi square 7.815 at 5% level.
The null hypothesis is not rejected.
We conclude that there is no difference between A and B in customer satisfaction.
| Chi-Square Test | ||||||||||
| Observed Frequencies | ||||||||||
| Column variable | Calculations | |||||||||
| Row variable | not satisfied | satisfied | Good satisfied | excellent satisfied | Total | fo-fe | ||||
| A | 20 | 40 | 70 | 20 | 150 | 2 | -2 | 4 | -4 | |
| B | 10 | 30 | 40 | 20 | 100 | -2 | 2 | -4 | 4 | |
| Total | 30 | 70 | 110 | 40 | 250 | |||||
| Expected Frequencies | ||||||||||
| Column variable | ||||||||||
| Row variable | not satisfied | satisfied | Good satisfied | excellent satisfied | Total | (fo-fe)^2/fe | ||||
| A | 18 | 42 | 66 | 24 | 150 | 0.2222 | 0.0952 | 0.2424 | 0.6667 | |
| B | 12 | 28 | 44 | 16 | 100 | 0.3333 | 0.1429 | 0.3636 | 1.0000 | |
| Total | 30 | 70 | 110 | 40 | 250 | |||||
| Data | ||||||||||
| Level of Significance | 0.05 | |||||||||
| Number of Rows | 2 | |||||||||
| Number of Columns | 4 | |||||||||
| Degrees of Freedom | 3 | |||||||||
| Results | ||||||||||
| Critical Value | 7.815 | |||||||||
| Chi-Square Test Statistic | 3.066 | |||||||||
| p-Value | 0.382 | |||||||||
| Do not reject the null hypothesis |
