EXAMPLE 24 Conducting the runs test for randomness

Test whether the sequence from Example 23 is random by conducting the runs test for randomness, using level of significance .

Solution

We know that the data are time-ordered, and that each data value represents one of two distinct outcomes. We may thus proceed with the hypothesis test.

  • Step 1 State the hypotheses.

  • Step 2 Find the critical values, and state the rejection rule. We have females and males, so the small-sample case applies ( and ). In Appendix Table L we find the row with and the column with , giving us the critical values and (see Figure 26). We will reject if or if .

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    Figure 14.26: FIGURE 26 Finding the critical values for the runs test for randomness.
  • Step 3 Find the value of the test statistic. We have the small-sample case, so the test statistic is simply the number of runs, :

  • Step 4 State the conclusion and the interpretation. Because is not and is not , we do not reject . There is insufficient evidence that the sequence is not random.

NOW YOU CAN DO

Exercises 9–20.