Test scores of ten individuals before and after a training p

Test scores of ten individuals before and after a training program are shown below.

Individual

Score After
the Program

Score Before
the Program

1

57

59

2

62

57

3

60

60

4

63

66

5

69

68

6

63

59

7

74

72

8

56

52

9

64

58

10

64

63

Question 10

Question text

What is the sum of positive signed ranks (T⁺)?

Select one:

a. 71.25

b. 14.52

c. 8.44

d. 22.50

e. 36.50

Question 11

Question text

The mean µ_T is

Select one:

a. 22.50

b. 71.25

c. 8.50

d. 14.52

e. 8.44

Question 12

Question text

The value of _T is

Select one:

a. 22.50

b. 8.44

c. 71.25

d. 8.50

e. 14.52

Individual	Score After the Program	Score Before the Program
1	57	59
2	62	57
3	60	60
4	63	66
5	69	68
6	63	59
7	74	72
8	56	52
9	64	58
10	64	63

Solution

Label

Difference

Rank

Signed Rank

1

-2

3.5

-3.5

2

5

8

8

3

-3

5

-5

4

1

1.5

1.5

5

4

6.5

6.5

6

2

3.5

3.5

7

4

6.5

6.5

8

6

9

9

9

1

1.5

1.5

( 0 difference is omitted)

Wilcoxon Signed Rank Test

variables:

Score After - Score Before

36.5

sum of positive ranks

8.5

sum of negative ranks

9

n

22.500

expected value

8.441

standard deviation

1.659

z

.0972

p-value (two-tailed)

n=9

Mean = n(n+1)/4 =9*10/4=22.5

Sd =sqrt(n*(n+1)(2n+1))/24) =sqrt(9+10+19/24) =8.44

Question 10

What is the sum of positive signed ranks (T⁺)?

Select one:

a. 71.25

b. 14.52

c. 8.44

d. 22.50

e. 36.50

Question 11

The mean µ_T is

Select one:

a. 22.50

b. 71.25

c. 8.50

d. 14.52

e. 8.44

Question 12

The value of _T is

Select one:

a. 22.50

b. 8.44

c. 71.25

d. 8.50

e. 14.52

Label	Difference	Rank	Signed Rank
1	-2	3.5	-3.5
2	5	8	8
3	-3	5	-5
4	1	1.5	1.5
5	4	6.5	6.5
6	2	3.5	3.5
7	4	6.5	6.5
8	6	9	9
9	1	1.5	1.5