Test the following sequence for randomness. B A A A A B A B B B B A A A
You may use the following abbreviated table of critical values for runs (at = .05).Reject the null
Hypothesis if the number of runs is less than or equal to the smaller value or greater than or equal to the
Larger value.
A)Do not reject because the test value 6 is not between the critical values 3 and 11
B)Do not reject because the test value 5 is between the critical values 3 and 12
C)Do not reject because the test value 6 is between the critical values 3 and 12
D)Reject because the test value 5 is not between the critical values 3 and 11

Question

Test the following sequence for randomness. B A A A A B A B B B B A A A
You may use the following abbreviated table of critical values for runs (at = .05).Reject the null
Hypothesis if the number of runs is less than or equal to the smaller value or greater than or equal to the
Larger value. 
A)Do not reject because the test value 6 is not between the critical values 3 and 11 
B)Do not reject because the test value 5 is between the critical values 3 and 12 
C)Do not reject because the test value 6 is between the critical values 3 and 12 
D)Reject because the test value 5 is not between the critical values 3 and 11

Quizplus · Accepted Answer

To test for randomness, we use the runs test. We count the runs in the sequence, that is the number of times the sequence changes from A to B or B to A. In this case, there are 6 runs: B, A, B, A, B, A. The critical values for runs at a significance level of .05 are 3 and 12. Since our test value of 6 falls between these critical values, we cannot reject the null hypothesis that the sequence is random. Therefore, the best choice is C. To test for randomness using the runs test, we need to count the number of runs (groups of consecutive identical letters) in the sequence. In this case, we have 6 runs: BBB, AAAA, BB, AAAAA, and AAA. The critical values for runs at α = .05 and n = 13 are 3 and 12. Since our test value of 6 falls between these critical values, we cannot reject the null hypothesis of randomness. Therefore, the best answer is C) Do not reject because the test value 6 is between the critical values 3 and 12.

Test the Following Sequence for Randomness