A family doctor wants to determine if the distributions of HDL cholesterol in males for the age groups 20 to 29 years, 40 to 49 years, and 60 to 69 years old are different. He obtains a simple random sample of 12 individuals from each age group and determines their HDL cholesterol. The results are presented in Table 15. Do the data indicate the distributions vary depending on age? Use the \(\alpha=0.05\) level of significance.

Approach Verify that the requirements needed to perform the Kruskal-Wallis test are satisfied. We then proceed to follow Steps 1 through 5.

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Table 15 Age (yr) Subject Number 20 to 29 40 to 49 60 to 69 1 54 (29) 61 (31.5) 44 (18) 2 43 (16) 41 (14) 65 (34.5) 3 38 (11.5) 44 (18) 62 (33) 4 30 (2) 47 (21) 53 (27.5) 5 61 (31.5) 33 (3) 51 (26) 6 53 (27.5) 29 (1) 49 (22.5) 7 35 (7.5) 59 (30) 49 (22.5) 8 34 (4.5) 35 (7.5) 42 (15) 9 39 (13) 34 (4.5) 35 (7.5) 10 46 (20) 74 (36) 44 (18) 11 50 (24.5) 50 (24.5) 37 (10) 12 35 (7.5) 65 (34.5) 38 (11.5)