Question

Random samples were drawn from three independent populations. The results are shown in the accompanying table. Use Table 3. Sample 1 12 95 115 110 9 Sample 2 10 85 105 80 75 90 Sample 3 72 65 10 76 66 55 a. Specify the competing hypotheses to test whether some differences exist between the medians. He: m-23HA: Not all population medians are equal. оне: m1 Z m2 m3; MA: All population medians are equal. He: m 2 3 HA: All population medians are equal b. Calculate the value of the test statistic H. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) Test statistic c-1. Find the p-value. Op-value 0.01 0.01 s p-value0.025 o 0.025 pvalue < 0.05 0 0.055 pvalue < 0.10 p-value 0.10

Answer 1

a) Ho: $\pi$1=$\pi$2=$\pi$3 ; Ha: Not all population medians are equal

b)

Rank Type sample 1 sample 1 sample 1 sample 1 sample 1 sample 2 sample 2 sample 2 sample 2 sample 2 sample 2 sample 3 sample 3 sample 3 sample 3 sample 3 sample 3 score 17 95 115 110 16 15 100 85 105 12.5 14 75 72 4 2 12.5 100 1 sample 1 sample 2 sample 3 2R1 68.5 R2 28.5 17 test stast:H- 8.6075

test statistic H =8.608 (try 8.607 if this comes wrong)

c-1)0.01 < p value <0.025

c-2)

Yes since we reject Ho