Question

Question 8                                                                                                                 10

A psychologist wishes to construct a true-false examination containing 30 questions. She desires the sequence of correct responses to be random so that nobody taking the examination can merely guess at the answers by following a particular pattern. The following sequence is obtained:

F T T T   F   T   F F F T T T T   F F F T T T T   F F T T T   F F   T   F F

Apply appropriate statistical testing procedures to determine if the sequence is non-random. [Use α=0.1]

Answer 1

Here we use the Run test.

The null and the alternative hypotheses are given by

The pattern is random

The pattern is not random

Total number of true answers(n1)=16

Total number of false answers(n2)=14

The number of runs for T is 6

The number of runs for F is 7

Total number of runs(r)=6+7=13

The critical value for significance level 0.05 is 23

As the observed value is less than the critical value, we reject the null hypothesis at 5% level of significance ; thus we reject the null hypothesis at 10% level of significance and hence conclude that the sequency is non - random at significance level 0.1

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