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Question 541:



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So we need to compare two standard deviations here. To do so we can use the critical  values from the F-distribution (a family of distributions like the t-distribution based on the sample size). This is also called the F-test.
1. The variance is equal to the standard deviation squared, providing us with variances of 15.21 and 12.25
2. The ratio is 15.21/12.25= 1.241 on 9 degrees of freedom in the numerator and 7 in the denominator. 
3. We can use the excel function =FDIST(1.241,9,7) =.396 which provides the 1-tailed probability. We need the 2-tailed probability so we multiply this value times 2 = .793, which is our p-value.
4. Since our rejection criteria is .05 and the p-value .792  is much greater than .05, we do NOT reject the null hypothesis (which was the variances are equal) so we cannot conclude that there is more variation in the oil stock.

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.

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