Question

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

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

Use a .05 level of significance. Use Table 1 of Appendix B.

a. What is the sum of the ranks for Swimming, Tennis and Cycling (to the nearest whole number)?

Sum of Rank Swimming
Sum of Rank Tennis
Sum of Rank Cycling

b. What is the value of the test statistic (to 2 decimals)?

How many degrees of freedom?

c. What is the -value?

- Select your answer -less than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10greater than .10

Do these data indicate differences in the amount of calories burned for the three activities?

- Select your answer - Yes  No

What is your conclusion?

- Select your answer -Conclude that the populations of calories burned by the three activities are identical.Conclude that the populations of calories burned by the three activities are not identical

Answer 1

Here we use the non parametric test for ANOVA i.e. Kruskal-Wallis test for testing whether the three different activities (Swimming, Tennis, Cycling) burn down the calories identically or not.

Null hypothesis- populations of calories burned by the three activities are identical

Alternative Hypothesis- populations of calories burned by the three activities are not identical

There are 15 units in the data. So we assign ranks to each unit as the highest value with highest rank i.e. 15. They are;

Swimming	ranks		Tennis	ranks		Cycling	ranks
415	10		385	6		408	9
380	5		485	14		250	2
425	11		450	13		295	4
400	7		120	1		402	8
427	12		530	15		268	3

(A)

Sum of Rank Swimming =45
Sum of Rank Tennis= 49
Sum of Rank Cycling = 26 (B) The test statistic used is H is calculated and is distributed as with 14 degrees of freedom where i

So the calculation will be

The critical value of at 2 degrees of freedom and 5% level of significance is 5.991.

Since the calculated value of H is 3.02 and is smaller than critical value 5.991. So we do not reject the null hypothesis.

(B) H statistic value = 3.02

(C)   Critical value = 5.991 i.e. is greater than 0.10.

(D)

These data does not indicate the differences in the amount of calories burned for the three activities.

The decision is that we do not reject the null hypothesis i.e. there is no significant difference among the means of calories burned by the three activities.

So we conclude that populations of calories burned by the three activities are identical.

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