Question

As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Trial Barth Tornado Reiser Shaw

1 43 37 41 43
2 46 38 45 45
3 43 39 42 46

Data are analyzed by One-Way Anova. The conclusion is:

a) at the 0.01 level of significance, the mean speeds for the 4 brands are all the same.
b) at the 0.05 level of significance, there is no difference between mean speeds for the 4 brands.
c) at the 0.05 level of significance, the mean speeds for the 4 brands are not significantly different from 0.
d) at the 0.01 level of significance, the mean speeds for the 4 brands are not all the same.

Answer 1

Ans)

a)At 5% L.O.S

One-way ANOVA: 1, 2, 3, 4

Method

Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
Factor 4 1, 2, 3, 4

Analysis of Variance

Source DF Seq SS Contribution Adj SS Adj MS F-Value P-Value
Factor 3 81.33 79.22% 81.33 27.111 10.17 0.004
Error 8 21.33 20.78% 21.33 2.667
Total 11 102.67 100.00%

Model Summary

S R-sq R-sq(adj) PRESS R-sq(pred)
1.63299 79.22% 71.43% 48 53.25%

Means

Factor N Mean StDev 95% CI
1 3 44.00 1.73 ( 41.83, 46.17)
2 3 38.000 1.000 (35.826, 40.174)
3 3 42.67 2.08 ( 40.49, 44.84)
4 3 44.667 1.528 (42.493, 46.841)

Pooled StDev = 1.63299

conclusion:at the 0.05 level of significance, there is difference between mean speeds for the 4 brands

b)at 1 % L.O.S

One-way ANOVA: 1, 2, 3, 4

Method

Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level α = 0.01

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
Factor 4 1, 2, 3, 4

Analysis of Variance

Source DF Seq SS Contribution Adj SS Adj MS F-Value P-Value
Factor 3 81.33 79.22% 81.33 27.111 10.17 0.004
Error 8 21.33 20.78% 21.33 2.667
Total 11 102.67 100.00%

Model Summary

S R-sq R-sq(adj) PRESS R-sq(pred)
1.63299 79.22% 71.43% 48 53.25%

Means

Factor N Mean StDev 99% CI
1 3 44.00 1.73 ( 40.84, 47.16)
2 3 38.000 1.000 (34.837, 41.163)
3 3 42.67 2.08 ( 39.50, 45.83)
4    3 44.667 1.528 (41.503, 47.830)

Pooled StDev = 1.63299

CONCLUSION:at the 0.01 level of significance, the mean speeds for the 4 brands are not all the same.

ANSWER :

"d) at the 0.01 level of significance, the mean speeds for the 4 brands are not all the same".