To investigate the effect of sleep on basal metabolism, seven college students w

Question

To investigate the effect of sleep on basal metabolism, seven college students who averaged seven or more hours of sleep a night (Group A), and five students who averaged less than seven hours of sleep a night (Group B), were examined and their basal metabolism recorded as shown below.

Since it was not clear whether the assumptions for a t-test were valid, the researcher decided to employ nonparametric methods. Use the Wilcoxon rank sum procedure to determine whether the metabolism measurements for Group A are significantly higher than those of Group B. Use Type 1 error = 0.05.

Group A 36 38 36 29 32 34 37 Group B 30 34 31 35 33

Explanation / Answer

First, we put both samples together and organize it in ascending order, which is shown in the table below:

Sample

Value

1

29

2

30

2

31

1

32

2

33

1

34

2

34

2

35

1

36

1

36

1

37

1

38

Now, that the values that are in ascending order are assigned ranks to them, taking care of assigning the average rank to values with rank ties

Sample

Value

Rank

Rank (Adjusted for ties)

1

29

1

1

2

30

2

2

2

31

3

3

1

32

4

4

2

33

5

5

1

34

6

6.5

2

34

7

6.5

2

35

8

8

1

36

9

9.5

1

36

10

9.5

1

37

11

11

1

38

12

12

The sum of ranks for sample 1 is:

R_1 = 1 + 4 + 6.5 + 9.5 + 9.5 + 11 + 12 = 53.5R1=1+4+6.5+9.5+9.5+11+12=53.5

and the sum of ranks of sample 2 is:

R_2 = 2 + 3 + 5 + 6.5 + 8 = 24.5R2=2+3+5+6.5+8=24.5

Hence, the test statistic is R = R_1 = 53.5R=R1=53.5.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H0: Median (Difference) = 0

Ha: Median (Difference) >> 0

(2) Rejection Region

The critical value for the significance level provided and the type of tail is Rc=17, and the null hypothesis is rejected if R17.

(3) Decision about the null hypothesis

Since in this case R = 53.5 > 17, there is not enough evidence to claim that the population median of differences is greater than 0, at the 0.05 significance level.

Kindly Upvote if Helpful :)

Sample

Value

1

29

2

30

2

31

1

32

2

33

1

34

2

34

2

35

1

36

1

36

1

37

1

38

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