EXAMPLE 3 Small-sample sign test for the population median

For the data from Example 2, use the sign test to determine whether the population median number of hurricane-related deaths per year is less than 50, using level of significance .

Solution

From Example 1, we know that the data come from a random sample, which is the only condition for conducting the sign test. Thus, we may proceed.

  • Step 1 State the hypotheses. the hypotheses are

    where represents the population median number of hurricane-related deaths per year.

  • Step 2 Find the critical value and state the rejection rule. The total number of plus signs and minus signs is , which is not greater than 25, so we use the small-sample case. We have a one-tailed test, with and , which gives us (Figure 2). The rejection rule is to reject if .

    image
    Figure 14.2: FIGURE 2 Using Appendix Table I to find the critical value .

  • Step 3 Find the value of the test statistic. We have a left-tailed test, and so, from Table 3, our test statistic is

    14-9

  • Step 4 State the conclusion and the interpretation. The value of our test statistic is , which is ≤1, so we reject . Evidence exists that the population median number of hurricane-related deaths is less than 50 per year.

NOW YOU CAN DO

Exercises 9–16.