To test if the mileage of three different makes of cars is the same, randomly selected trips on those makes are recorded and the data is shown below for the miles per gallon of the trips
Make 1 |
Make 2 |
Make 3 |
29.9 |
45.8 |
34.8 |
31.1 |
40.3 |
41.4 |
23.5 |
36.6 |
40 |
30.5 |
29 |
37.6 |
35.4 |
40.3 |
41.4 |
33 |
33 |
48.1 |
28.5 |
35.5 |
37.2 |
32.4 |
34.9 |
44.1 |
25.7 |
31 |
42 |
40.3 |
44.9 |
Use one way ANOVA to test if the means of the mileage of the all
the cars of these make are the same. Assume that the data may be
treated as simple random samples.
Show
1. The verification that the ratio of the largest to the lowest of the standard deviations is less than 2.
2. There are no extreme outliers.
State the P_value and your conclusion
.
Anova: Single Factor | ||||||
SUMMARY | ||||||
Groups | Count | Sum | Average | Variance | ||
Make 1 | 9 | 270 | 30 | 13.5475 | ||
Make 2 | 10 | 366.7 | 36.67 | 25.76011111 | ||
Make 3 | 10 | 411.5 | 41.15 | 15.75166667 | ||
ANOVA | ||||||
Source of Variation | SS | df | MS | F | P-value | F crit |
Between Groups | 593.1057241 | 2 | 296.5528621 | 15.99709206 | 2.95567E-05 | 3.369016 |
Within Groups | 481.986 | 26 | 18.53792308 | |||
Total | 1075.091724 | 28 |
a)
highest sd = 25.76
lowest = 13.5475
highest/lowest = 25.76/13.5475 < 2
p-value = 2.95567*10^(-5) << 0.05
hence there is significant difference between groups
To test if the mileage of three different makes of cars is the same, randomly selected...