Corrosion Resistance Test for Steel Conduit: Hypothesis Setup and Results

[needhelp83]

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 \overline{x} = 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: \mu=50
Ha: \mu>50

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

 

[statdad]

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.

 

[needhelp83]

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.

 

[needhelp83]

Is this what you were referring to statdad?

 

[statdad]

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