SOLUTION: The mean length of a small counterbalance bar is 43 millimeters. The production supervisor is concerned that the adjustments of the machine producing the bars have changed. He as

Question 136703: The mean length of a small counterbalance bar is 43 millimeters. The production supervisor is concerned that the adjustments of the machine producing the bars have changed. He asks the Engineering Department to investigate. Engineering selects a random sample of 12 bars and measures each. The results are reported below in millimeters:
42 39 42 45 43 40 39 41 40 42 43 42
Is it reasonable to conclude that there has been a change in the mean length of the bars? Use the .02 level of significance. Show all 5 steps � interpret your conclusion!

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The mean length of a small counterbalance bar is 43 millimeters. The production supervisor is concerned that the adjustments of the machine producing the bars have changed. He asks the Engineering Department to investigate. Engineering selects a random sample of 12 bars and measures each. The results are reported below in millimeters:
42 39 42 45 43 40 39 41 40 42 43 42
Is it reasonable to conclude that there has been a change in the mean length of the bars? Use the .02 level of significance.
------------
Ho: u=43 mm
Ha: u is not 43 mm
--------------------
x-bar =41.5
s = 1.78377
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Comment: I used a T-test because n=12
--------------------------------
test statistic is t=63.504
p-value = 1.82 x 10^-15 (or very, very small)
---------------------------------
Conclusion: Since p is less than alpha=2%, Fail to reject Ho.
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Cheers,
Stan H.
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