Question 1172028: The mean length of certain bar for construction is supposed
to be 43mm. There is a concern that the length has changed,
12 bars were selected at random for a study. The following lengths were recorded: 44, 39, 45, 43, 40, 39, 41, 40, 42, 43, 42, 42 in mm.
Do you agree that there has been a change in the mean length? Use α= 1%
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the mean is supposed to be 43.
you find the mean of the sample to be equal to 41.66666
you find the standard deviation of the sample to be 1.92275
the sample size is 12 elements.
the standard error is equal to the standard deviation of the sample divided by the sample size = 1.92275 / sqrt(12) = .55505
the t-score with 11 degrees of freedom is equal to (41.66666 - 43) / .55505 = -2.40219.
the area to the left of a t-score of -2.40219 with 11 degrees of freedom is equal to .017548.
this is greater than .01 if a one tailed test, or .005 if a two tailed test.
therefore, there is not enough evidence to determine that the actual mean is not 43.
the difference is determined to be due to random variation in the mean of a sample of size 12.
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