Statistics

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see the attachment

14.2
A company had received complaints that the disks provided by the company failed to work properly after extended use. The company has decided to investigate the complaint. Data are collected on the time to failure for disks from their current supplier and two alternate suppliers. The data are shown below:

Current supplier Alternative 1 supplier Alternative 2 supplier

486 489 508
490 489 510
491 491 517
491 492 506
494 492 515
494 492 520
496 492 503
498 493 524
498 493 515
502 494 503
504 495 507
505 496 515
506 497 509
507 497 518
508 497 495
510 498 499
514 499 510
515 502 503
527 503 533
498 505 517

a) What is the response variable and what is the factor?
The response variable is the time to failure for disks, and the there is only one factor that is the supplier.
b) Ho many levels of the factor are being studied?
There are 3 levels of the factor are being studied. They are Current supplier; Alternative 1 supplier and Alternative 2 supplier. For each level we have 20 sample units.
c) Is there any difference in the average time to failure of the disks from the 3 different suppliers? If so, which ones are different?
We can get the ANVOA table by Excel as follows:

Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Column 1 20 10034 501.7 102.3263
Column 2 20 9906 495.3 20.11579
Column 3 20 10227 511.35 81.50263
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 2611.233 2 1305.617 19.20545 4.21E-07 3.158846
Within Groups 3874.95 57 67.98158

Total 6486.183 59

Since the p-value is so small that we can reject the hypothesis that there are no differences between the three levels. That mean there must be some differences between three levels.
Now we need to computer the difference between levels:
Let denote the level mean of Current supplier; denote the level mean of Alternative 1 supplier and denote the level mean of Alternative 2 supplier. So from the ANOVA table we know that =501.7, =495.3 and =511.35.
Let - , - , - . So = - =6.4,
= - =-9.65, = - =-16.05. And =sqrt(67.98158*0.1)=2.61
So we construct the null and alternative hypothesis as follows:
H0: =
Ha: (i j)
As we know ...