C. There are not enough data points to reach a conclusion D. The tied value make

Question

C. There are not enough data points to reach a conclusion D. The tied value makes the analysis suspect 3. An investigator wants to test if there is a difference in endotoxin levels in children who are exposed to endotoxin as a function of their proximity to operating farms. The following are endotoxin levels in units per milligram of dust sampled from children's mattresses, organized by children's proximity to farms. Within 5 Miles 5-24.9 Miles 25-49.9 Miles 50 Miles or More 54 62 78 90 70 28 42 39 8 65 37 29 30 50 53 36 19 22 28 27 Total Sample (Ordered Smallest to La 50+ Miles Miles Miles 50+ Miles 5 5-24.9 25-49.9 s 5 Miles Miles Miles M 5-24.925-49.9 HLTH 501 Apply the Kruskal Wallis test at a 5% level of significance. Alpha- df- Critical valuc Based on comparing H to the critical value to the Critical value which of the following is (are) true? A. There is significant evidence at alpha-0.05 t o show that the populations of endotoxin levels in children living varying distances from operating farms are not equal endotoxin levels in children living varying distances from operating farms are not equal B. There is not significant evidence at alpha -0.05 to show that the populations of C. There are not enough data points to reach a conclusion. D. The tied value makes the analysis suspect

Explanation / Answer

Null hypothesis: Null hypothesis assumes that the samples (groups) are from identical populations.

Alternative hypothesis: Alternative hypothesis assumes that at least one of the samples (groups) comes from a different population than the others.

Alpha level = 0.05

Here Degree of freedom = k-1 = 3

Criticical value = CHIINV (4 , 0.05) = 7.815

Here N = 20 and n = 5

H = 12/(N(N+1)) * (T2/n) - 3(N+1)

H = 12/(20 * 21) * [842/5 + 60.52/5 + 472/5 + 18.52/5] - 3 * (20 + 1)

H = 75.8143 - 63 = 12.814

so here H > Critical value so we can reject the null hypothesis and can conclude that Option A is correct.

Total samples (smallest to largeest) < 5 miles 5 - 24.9 miles 25-49.9 miles 50+ miles < 5 miles 5 - 24.9 miles 25-49.9 miles 50+ miles 54 28 37 36 54 28 29 19 62 42 29 19 62 39 30 22 78 39 30 22 78 42 37 27 90 81 50 28 70 65 50 28 70 65 53 27 90 81 53 36

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