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Setting up Hypotheses

  1. Sep 10, 2009 #1
    Ok...this is one of my first hypothesis test, so I wanted to make sure I am doing everything correctly. Thanks for any suggestions.

    To obtain information on the corrosion-resistance properties of a certain type of steel conduit, 45 specimens are buried in soil for a 2-yr period. The maximum penetration (in mils) for each specimen is then measured, yielding a sample average penetration of [tex]\overline{x}[/tex] = 52.7 and a sample standard deviation of s = 4.8. The conduits were manufactured with the specification that true average penetration be at most 50 mils. They will be used unless it can be demonstrated conclusively that the specification hasn't been met.

    Ho: [tex]\mu[/tex]=50
    Ha: [tex]\mu[/tex]>50

    Test criteria:
    Z=[tex]\frac{\overline{x}-50}{s/\sqrt{n}}[/tex] = [tex]\frac{52.7-50}{4.8/\sqrt{45}}[/tex]= 3.77

    Significance level = 95%, so Z .05 = 1.645

    1.645>3.77 False
    Since 1.645 !> 3.77, we don't reject Ho.

    We cannot conclude that the specifications have not been met, so the corrosion resistance properties will be used.

    Thanks again for any help.
     
  2. jcsd
  3. Sep 10, 2009 #2

    statdad

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    Homework Helper

    a) The significance level would never be set to 95% - do you mean 5%?
    b) You've carried out your test incorrectly - go back and look at how the calculated test statistic and the critical value (this is the 1.645) should be used.
     
  4. Sep 10, 2009 #3
    a) The significance level would never be set to 95% - do you mean 5%?

    Yes, I meant 5%

    b) You've carried out your test incorrectly - go back and look at how the calculated test statistic and the critical value (this is the 1.645) should be used.

    Yes, I interpreted my notes wrong for the test statistic and critical value.

    It should be

    3.77 > 1.645

    Since 3.77 > 1.645 we reject Ho.


    We can conclude that the specifications have not been met, so the corrosion resistance properties will not be used.
     
  5. Sep 11, 2009 #4
    Is this what you were referring to statdad?
     
  6. Sep 11, 2009 #5

    statdad

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    Homework Helper

    Perfect - yes, now you have it. I see I missed an earlier question from you - sorry about that.
     
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