# Anova - ANOVA QUESTIONS QUESTION NO 15.22 Does the level of...

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ANOVA QUESTIONS QUESTION NO. 15.22 Does the level of success of publicly traded companies affect the way their board members are paid? Publicly traded companies were divided into four quarters using the rate of return in their stocks to differtiate among the companies. The annual payment (in \$1,000s) to their board members was stored in file Xr 15-22. Can we infer that the amount of payment differs among the four groups of companies? ANSWER: Hypothesis: H o : The amount of payment do not differ in four groups; i.e. u 1 = u 2 = u 3 = u 4 H 1 : The amount of payment differs in four groups; i.e. u 1 ≠ u 2 ≠ u 3 ≠ u 4 Significance level: α = 0.05 Test Statistic: Because the population variance is unknown, and the objective is to compare mean of more than two popuations, so we use one way ANOVA test. Descriptives:

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Descriptives Amount of payment N Mean Std. Deviation Std. Error 95% Confidence Interval for Mean Minimum Maximum Lower Bound Upper Bound Company 1 30 74.1000 15.80997 2.88649 68.1965 80.0035 37.00 115.00 Company 2 30 75.6667 13.57313 2.47810 70.5984 80.7350 49.00 101.00 Company 3 30 78.5000 15.27619 2.78904 72.7958 84.2042 40.00 116.00 Company 4 30 81.3000 15.58547 2.84550 75.4803 87.1197 51.00 113.00 Total 120 77.3917 15.14984 1.38298 74.6532 80.1301 37.00 116.00 Test of Homogeneity of Variances: Hypothesis: H o : Variances of groups are equal. H 1 : Variances of groups are not equal. Significance level: α = 0.05 Test Results: Test of Homogeneity of Variances Amount of payment Levene Statistic df1 df2 Sig. .221 3 116 .882 [ Interpretation: Levene’s test was conducted to test the homogeneity of variances of amount of payment (in \$1,000) among four groups of companies. As p-value (.882 > α), we failed to reject Ho. Thus, the variances of groups are not equal. Test of Normality: Hypothesis:
H o : Distribution is normal. H 1 : Distribution is not normal. Significance level: α = 0.05 Test Results: Tests of Normality company_ quarters Kolmogorov-Smirnov a Statistic df Sig. payments 1st quarter .088 30 .200 * 2nd quarter .092 30 .200 * 3rd quarter .107 30 .200 * 4th quarter .087 30 .200 * Interpretation: Test of normality was conducted to test the distribution’s normality. Kolmogorov Smirnov test is significant (p-value = .200 > a) . Thus, there is significant evidence that distribution is normal. NOTE: As the assumptions of normality ad homogeneuity of variances are met, so it is good enough to run one way ANOVA test.

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