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Question 843:



No answer provided yet.In this question you need to determine whether two standard deviations are different. When comparing standard deviations you actually have to compare the variances instead. The variance is just the square of the standard deviation. To compare the variances we use the ratio and test it against a reference F-statistic.  The Null Hypothesis for this test is that the variances are equal. We will reject the Null if the 2-tailed p-value is less than .05.

Squaring the standard deviations gets us the two variances of  33.64 and 94.09 respectively. This gets us an F-ratio of 33.66/94.09 = 2.796. We evaluate the significance of this test statistic using n-1 degrees of freedom in the numerator and denominator, or 13-1 and 12-1 = 12 and 11.  If you don't have access to an inverse F-table, you can use the excel function =FDIST(2.796,12,11)  and we get the 1-tailed p-value of .045, making the 2-tailed p-value .091. Since the p-value is above our cut-off of .05 we fail to reject the Null Hypothesis. We conclude the standard deviation of 4 and 6 cylinder cars are the same.

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