## Question 527:

1## Answer:

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We can use the F-test, which is a ratio of the variances to test to see if there is a difference between variance.

- The variance is equal to the standard deviation squared, providing us with variances of 9.12 and 26.21
- The ratio is 26.21/9.12 = 2.874 on 24 degrees of freedom in the numerator and 24 in the denominator.
- We can use the excel function =FDIST(2.874,24,24) =.00614 which provides the 1-tailed probability. We need the 2-tailed probability so we multiply this value times 2 = .0123, which is our p-value.
- Since our rejection criteria is .05 and the p-value .0123 is less than .05, we reject the null hypothesis (which was the variances are equal) and conclude there is a difference between the variances, and therefore the standard deviations.

A note on using the F-test. There are multiple ways to test for unequal variances, the F-test is one way, however, it has been criticized as being too sensitive to outliers in the data (since the standard deviation is based on the mean and both are therefore affected by outliers). Other tests, such as the Levine test are recommended, however the raw data are needed for this test. Since the sample sizes are equal here, while there is evidence for differing variances, it is usually considered appropriate to proceed with t-tests and they can handle (are robust) to such a violation of homogeneity of variance.

See the attached excel file for calculations.