Question

Krusskal – Wallis Test Forty-minute workouts of one if the following activities three days a week will lead to a loss weight. The following sample data show the number of calories burned during 40-minute workouts for three different activities.

Swimming	Tennis	Cycling
408	415	385
380	485	250
425	450	295
400	420	402
427	530	268

a. At the 0.05 level of significance, is there evidence of a significant difference in the median amount of calories burned among the different activities?

b. What is your conclusion?

Answer 1

(a)

Ho: There is no significant difference between the median amount of calories

Ha: There is a significant difference between the median amount of calories

Calories	Group	Rank
250	Cycling	1
268	Cycling	2
295	Cycling	3
380	Swimming	4
385	Cycling	5
400	Swimming	6
402	Cycling	7
408	Swimming	8
415	Tennis	9
420	Tennis	10
425	Swimming	11
427	Swimming	12
450	Tennis	13
485	Tennis	14
530	Tennis	15

Sum of ranks:
Swimming	41
Tennis	61
Cycling	18

H = [12/{15(15 + 1)] [(41^2)/5 + (61^2)/5 + (18^2)/5] – 3(15 + 1) = 9.26

Critical χ2 value (Df = 2) = 5.9915

Since 9.26 > 5.9915, we reject Ho

(b)

There is a significant difference between the median amount of calories

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