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Unformatted text preview: at, although the population means were all equal, there is still some of variation between the sample means. Also in Scenario C there is still some natural variation within the samples, making the slight variation between the sample means hardly noticeable. The data in Scenario C do not provide evidence that the population means are different. Scenario C Samples from 3 populations whose means are all equal. Still some variability within each population. Very little differences between the sample means. F statistic very small. The F‐statistic will be sensitive to differences between the sample means. The larger the variation between the sample means, the larger the value of the F‐statistic and larger values of the F‐statistic provide more support for rejecting the null hypothesis. The variation between the sample means was greatest for Scenarios A and B compared to Scenario C. The natural variation within the samples was greatest for Scenario B compared to Scenarios A and C. The F‐statistic is the ratio of these two measures of variation: F Variation among sample means
Natural variation within groups So which scenario would you expect to result in the largest value of the F‐statistic? Provided below are the values of the F‐statistic for the test of equality of the population means. Scenario A (Ha is true) B (Ha is true) C (H0 is true) Value of F Statistic F = 80.4 F = 16.4 F = 0.17 p‐value 0.0000 0.01 0.84 Note the value of the F‐statistic is smallest and the p‐value the largest when the null hypothesis is true (Scenario C). For Scenarios A and B, the population means are different, but the smaller population standard deviation in Scenario A accentuates the differences by producing a larger F‐ratio and an extremely small p‐value. A larger F‐statistic value (and thus smaller p‐value) corresponds to more evidence that the population means are not all equal. 172 Com...
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