Question

1. For a test item with two response options (e.g., true/false), what is the probability of selecting the correct answer by chance?
2. Calculate the optimal level of difficulty for a test questions with two response options.   
3. For a test item with three response options, what is the probability of selecting the correct answer by chance?
4. Calculate the optimal level of difficulty for a test questions with three response options
5. For a test item with four response options, what is the probability of selecting the correct answer by chance?
6. Calculate the optimal level of difficulty for a test questions with four response options?
7. For a test item with five response options, what is the probability of selecting the correct answer by chance?
8. Calculate the optimal level of difficulty for a test questions with five response options.

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Answer 1

a).

For two response option - P(selecting correct answer) =( # of favourable outcomes/total # of outcomes) = 1/2 = 0.5

Level of difficulty is % of total group that got the answer correct.

Thus optimum level of difficulty for two response option is = 0.75

b). P (selecting correct answer) for three response option = 1/3 = 0.33

optimum level of difficulty for three response option is = 0.665

c).

P (selecting correct answer) for four response option = 1/4 = 0.25

optimum level of difficulty for three response option is = 0.625

d).

P (selecting correct answer) for five response option = 1/5 = 0.20

optimum level of difficulty for three response option is = 0.60