Test the following sequence of values for randomness with respect to being above or below the median. 4 6 3 8 5 7 5 7 3 7 9 1 3 8 5 Table of Critical Values for the Number of Runs, α = 0.05 Value of N₁ Value of n₂ 4 5 6 7 6 2 9 3 10 3 11 3 12 7 2 10 3 11 3 12 3 13 8 3 10 3 11 3 12 4 13 A) Reject the hypothesis that the sequence is random, because the test value 8 is between the critical values 3 and 12 B) Reject the hypothesis that the sequence is random, because the test value 7 is between the critical values 3 and 11 C) Do not reject the hypothesis that the sequence is random, because the test value 8 is between the critical values 3 and 11 D) Do not reject the hypothesis that the sequence is random, because the test value 7 is between the critical values 3 and 12

Question

Quizplus · Accepted Answer

To test for randomness with respect to being above or below the median, we need to count the number of runs in the sequence. A run is a sequence of consecutive values that are either all above or below the median. In this sequence, the median is 5. So we count the number of runs of values above 5 and the number of runs of values below 5. We get 5 runs of values above 5 and 4 runs of values below 5.

To determine if this result is statistically significant, we use the table of critical values for the number of runs at α = 0.05. The critical values for this sequence with n = 15 are 3 and 11. The test value for this sequence is 8, which is between the critical values 3 and 11. Therefore, we do not reject the hypothesis that the sequence is random with respect to being above or below the median. Answer choice C is correct.

Test the Following Sequence of Values for Randomness with Respect