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Math Help - [SOLVED] Statistics - Differance in mean problem

  1. #1
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    [SOLVED] Statistics - Differance in mean problem

    Hi, please give me a help to find the answer for the following statistic problem,

    As a production manager suppose you want to check whether the 3 filling
    machines have different mean filling times. If you have assign 15 similarly trained &
    experienced workers, 5 per machine, at the 5% level of significance, is there a
    difference in mean filling times?
    Machine 1 Machine 2 Machine 3
    25.40 23.40 20.00
    26.31 21.80 22.20
    24.10 23.50 19.75
    23.74 22.75 20.60
    25.10 21.60 20.40

    See the attached picture for better understanding of the problem
    Attached Thumbnails Attached Thumbnails [SOLVED] Statistics - Differance in mean problem-l5a4q1.jpg  
    Last edited by dhammikai; November 26th 2009 at 01:21 AM. Reason: attach the JPEG file
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  2. #2
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    Quote Originally Posted by dhammikai View Post
    Hi, please give me a help to find the answer for the following statistic problem,

    As a production manager suppose you want to check whether the 3 filling
    machines have different mean filling times. If you have assign 15 similarly trained &
    experienced workers, 5 per machine, at the 5% level of significance, is there a
    difference in mean filling times?
    Machine 1 Machine 2 Machine 3
    25.40 23.40 20.00
    26.31 21.80 22.20
    24.10 23.50 19.75
    23.74 22.75 20.60
    25.10 21.60 20.40

    See the attached picture for better understanding of the problem
    You can compare two machines at a time by setting H_0:\mu_1=\mu_2 for no difference between two machines, and h_1:\mu_1 \neq \mu_2 for there is significant difference between the two, using two tailed-test. In all tests, if -z_{0.05} < z > z_{0.05}, reject H_0; otherwise accept or withhold your decision.
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  3. #3
    MHF Contributor matheagle's Avatar
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    You should run an F test via ANOVA on this to test all three means at the same time.
    I just found this
    ANOVA Test
    I'm not sure if it's any good, but the idea is correct.
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  4. #4
    MHF Contributor matheagle's Avatar
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    Mean1 24.93 Variance1 1.0648
    Mean2 22.41 Variance2 1.483
    Mean3 20.59 Variance3 0.9205
    Variation Between 23.7486667 Variation Within 1.1561

    F-Statistic 20.5420523 P-Value 0.00063
    Conclusion Very strong evidence against the null hypothesis
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  5. #5
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    Thanks

    Hi, I gut a answer now thanks matheagle, novice for excellent explanations!
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  6. #6
    MHF Contributor matheagle's Avatar
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    I would not do a Bonferroni test, where you test pairs of means.
    http://www.itl.nist.gov/div898/handb...on4/prc473.htm
    You should test...

    H_0: \mu_i=\mu_j for all i,j

    vs.

    H_a: \mu_i\ne\mu_j for some i\ne j
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