ࡱ> 5@ 0Kbjbj22 . XXK2222222F, F 2Zg g g        $< R + 2g g g g g + 22@  g 22 g   22 & 0G# vq :  V 0   FF22222 (g g g g g g g + + FF$j FFjA stockbroker at critical securities reported that the mean rate of return on a sample of 10 oil stocks was 12.6 percent with a standard deviation of 3.9 percent. The mean rate of return on a sample of 8 utility stocks was 10.9 with a standard deviation of 3.5 percent . At .05 significance level can we conclude that there is more variation in the oil stocks? Let  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  be the variances of the return of oil and utility stocks respectively. Here we want to test the null hypothesis H0:  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4  against the alternative hypothesis H1:  EMBED Equation.DSMT4  >  EMBED Equation.DSMT4 . Let  EMBED Equation.DSMT4 and  EMBED Equation.DSMT4  be the sample standard deviation of the return of oil and utility stocks respectively. The test statistic for testing H0 is  EMBED Equation.DSMT4 , the F distribution with  EMBED Equation.DSMT4  degrees of freedom. From the given data,  EMBED Equation.DSMT4 = 10,  EMBED Equation.DSMT4 = 8,  EMBED Equation.DSMT4  = 3.9,  EMBED Equation.DSMT4  = 3.5 Thus the calculated value of  EMBED Equation.DSMT4  = 1.2416 Since the significance level is 0.05, using the F distribution with  EMBED Equation.DSMT4 = (9, 7) degrees of freedom, we get the critical value = 3.667 Thus the critical region of the test is F > 3.667 That is we reject the null hypothesis if F > 3.667. Here, F = 1.2416 < 3.667 So we fail to reject the null hypothesis Ho. Thus at .05 significance level we cannot conclude that there is more variation in the oil stocks P-value approach Using the F distribution with  EMBED Equation.DSMT4 = (9, 7) degrees of freedom, we get the P-value as P-value = P[ F > 1.2416] = 0. 3964 Since the level of significance EMBED Equation.DSMT4 = 0.05, we reject the null hypothesis  EMBED Equation.DSMT4  if the P-value < 0.05. Here the P-value = 0. 3964 > 0.05 So we do not reject the null hypothesis Ho. 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