Question 1206944: Test the given claim. Assume that a simple random sample is selected from a normally distributed population. Use either the P-value method or the traditional method of testing hypotheses.
Company A uses a new production method to manufacture aircraft altimeters. A simple random sample of new altimeters resulted in errors listed below. Use a 0.05 level of significance to test the claim that the new production method has errors with a standard deviation greater than 32.2 ft, which was the standard deviation for the old production method. If it appears that the standard deviation is greater, does the new production method appear to be better or worse than the old method? Should the company take any action?
-44, -79, -21, -70, -41, 14, 17, 55, -8, - 54, - 109, - 109
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the old method has a standard deviation of 32.2 feet.
the new method has a standard deviation of 51.0 feet.
i think the f-test would be used to see if the standard deviations are comparable.
i did an f-test online that compares variances (variance = square of standard deviation) and it came back with the results that the variances are far enough away to be considered statistically significant at an alpha of .05.
the f-test calculator i used can be found at https://www.statskingdom.com/220VarF2.html
it compares the standard deviation of group 1 to the standard deviation of group 2.
i assumed the sample sizes were the same since i didn't have a sample size for the test standard deviation of 32.2.
in general, a larger standard deviation would provide an inferior result.
based on this, i don't believe the new method is superior to the old method and i would probably stick with the old method.
significant means there is a very low probability that the differences are due to chance variations in the statistics between the two data sets.
given that there is a statistically significant difference, it is logical to assume that a smaller standard deviation is superior to a larger standard deviation when comparing data sets.
i played with the sample size of group 1 (had a standard deviation of 32.2).
the results were more significant as i increased the sample size, indicating more support for the fact that there was a significant differenct between 32.2 and 51.0.
i'm not sure if this is the right way to do it, but it makes sense to use the f-test to see if the differences in standard deviation between two data sets is significant or not.
best i can do.
hope it helps.
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