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    A) What is the response variable and what is the factor?

    b) Ho many levels of the factor are being studied?

    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?

    d) What is your recommendation to the company and why?

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    https://brainmass.com/statistics/hypothesis-testing/statistics-factors-variables-5892

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    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 ...

    Solution Summary

    The response variable and what is the factor are determined. The levels of the factor are being studied are given.

    $2.49

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