A computer manufacturer plans to unveil a new and faster personal computer. The new machine is clearly faster but initial tests indicate there is more variation in the processing time. The processing time depends on the program being run, the amount of input data and the amount of output. A sample of 16 computer runs, covering a range of production jobs, showed that the standard deviation of the processing time was 22 (hundredths of a second) for the new machine and 12 (hundredths of a second) for the current machine. At the .05 significance level, can we conclude that there is more variation in the processing time of the new machine?
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Yes, we can conclude that there is more variation in the processing time of the new machine.
To test this, we can use the F-test for comparing variances. The F-test statistic is the ratio of the two variances, which in this case is (22/12)^2 = 3.36.
The critical value for the F-test at the .05 significance level with 15 degrees of freedom in the numerator and 15 degrees of freedom in the denominator is approximately 2.51.
Since our test statistic (3.36) is greater than the critical value (2.51), we reject the null hypothesis that the variances are equal. Therefore, we conclude that there is more variation in the processing time of the new machine.
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