Question 1: A test has a mean of 30 and a standard deviation of five.

Jackie has scored in the 57th percentile.
Ethan has a T score of 70.
Lan has obtained a z score of –0.2.
Salvatore has received a raw score of 27.
On the basis of the information provided, answer the following questions:

Who has scored the highest?
Who has scored the lowest?
Question 2: The following table displays fictitious data for a four-option multiple-choice question:

Options

Item

Groups

A

B

C

D

p-value

1.

Upper
Middle
Lower

1
0
1

1
18
15

24*
25*
4*

1
5
7

.52

2.

Upper
Middle
Lower

1
0
2

25*
42*
23*

0
3
1

1
3
1

.88

3.

Upper
Middle
Lower

19
32
16

7*
8*
8*

1
3
2

0
5
1

.23

The data was collected from a hundred individuals classified on the basis of class—upper, middle, or lower. This classification was done on the basis of the total scores using Kelly’s 27% rule. Correct options have been marked with an asterisk for each question.

On the basis of the data provided, answer the following question:

• Are there any faulty distractors? Why do you believe the distractors are working (or not working) properly?

Question 3: The following table displays fictitious data from a ten-item multiple-choice exam:

Item

Option A

Option B

Option C

Option D

Option E

p-value

1

667

187

37

30

10

.72

2

840

1

76

9

5

.90

3

561

233

46

88

4

.60

4

923

3

3

3

0

.99

5

876

0

12

24

20

.94

Each question has five options. The table provides the number of individuals choosing each option, the p-value, and the D-index. The correct answer for each question item is option A.

On the basis of the data provided, answer the following questions:

Which items should be removed or revised and why?
Which distractors, in which items, are working well, and why?

Sample Solution