The following information is available for two samples drawn from independent no

Question

The following information is available for two samples drawn from independent normally distributed populations. Population A n 10 S 151.4 Population B n 10 S 104.9 # ? ? What is the upper critical value for F if the level of significance, c , is 0.05 and the alternative hypothesis is H1: ? Click here to view page 1 of the F table. Click here to view page 2 of the F table Click here to view page 3 of the F table. Click here to view page 4 of the F table The upper critical value for FisRoud to two decimal places as needed.)

Explanation / Answer

For the samples drawn from independent normally distributed population, given that nA is the degree of freedom of numerator with value 10 and nB is the degree of freedom of denominator with value 10. The level of significance ? is 0.05 which indicates a 5% risk of concluding that a difference exists when there is no actual difference.

Now, the upper critical value for F corresponding to nA and nB at 5% significance level is 2.98. Also for a right tail distribution the critical value for 0.025 corresponding to F0.025,(9,9) is (4.026,4.026).

Hence by performing the calculation [151.4/104.9)1/4.026,(151.4/104.9)4.026] we get the range [0.358,5.81]. therefore a 95% confidence interval for the ratio of the population variances ranges from 0.358 to 5.81.

We can conclude that in the alternative hypothesis ?1/?2?1 which means 1 should not be included in the population variance range.Since the interval includes the value 1, we cannot reject the hypothesis H0.

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