Jacob Lee is a frequent traveler between Los Angeles and San Diego. For the past month, he wrote down the flight times in minutes on three different airlines. The results are:
Goust | Jet Red | Cloudtran |
51 | 50 | 52 |
51 | 53 | 55 |
52 | 52 | 60 |
42 | 62 | 64 |
51 | 53 | 61 |
57 | 49 | 49 |
47 | 50 | 49 |
47 | 49 | |
50 | 58 | |
60 | 54 | |
54 | 51 | |
49 | 49 | |
48 | 49 | |
48 | 50 | |
1. Null hypothesis:
2. Alternate hypothesis:
3. State the decision rule for 0.05 significance level.
4. Develop a 95% confidence interval for the difference in the means between Goust and Cloudtran.
using minitab>Stat>ANOVA >one way ANOVA
we have
One-way ANOVA: Goust, Jet Red, Cloudtran
Method
Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level α = 0.05
Rows unused 6
Equal variances were assumed for the analysis.
Factor Information
Factor Levels Values
Factor 3 Goust, Jet Red, Cloudtran
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Factor 2 127.1 63.56 3.04 0.062
Error 32 669.9 20.93
Total 34 797.0
Model Summary
S R-sq R-sq(adj) R-sq(pred)
4.57526 15.95% 10.70% 0.00%
Means
Factor N Mean StDev 95% CI
Goust 14 50.50 4.47 (48.01, 52.99)
Jet Red 14 52.07 3.83 (49.58, 54.56)
Cloudtran 7 55.71 6.05 (52.19, 59.24)
Pooled StDev = 4.57526
Tukey Pairwise Comparisons
Grouping Information Using the Tukey Method and 95% Confidence
Factor N Mean Grouping
Cloudtran 7 55.71 A
Jet Red 14 52.07 A B
Goust 14 50.50 B
Means that do not share a letter are significantly different.
Tukey Simultaneous Tests for Differences of Means
Difference SE of Adjusted
Difference of Levels of Means Difference 95% CI T-Value
P-Value
Jet Red - Goust 1.57 1.73 (-2.68, 5.83) 0.91 0.639
Cloudtran - Goust 5.21 2.12 ( 0.00, 10.43) 2.46 0.050
Cloudtran - Jet Red 3.64 2.12 (-1.57, 8.85) 1.72 0.213
Individual confidence level = 98.06%
1. the Null hypothesis :
2. Alternate hypothesis: At least one mean is different
3. since p value of F stat is 0.062 which is greater than 0.05 so we dont reject Ho and conclude All means are equal
4. a 95% confidence interval for the difference in the means between Goust and Cloudtran. is (-10.43 , 0.00)
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