Example 3

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 $M$ number of hurricane-related deaths per year is less than 50, using level of significance $α = 0.05$ .

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

$\begin{matrix} H_{0} : M = 50 & versus & H_{α} : M < 50 \end{matrix}$

where $M$ 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 $n = 7 + 1 = 8$ , which is not greater than 25, so we use the small-sample case. We have a one-tailed test, with $α = 0.05$ and $n = 8$ , which gives us $S_{cirt} = 1$ (Figure 2). The rejection rule is to reject $H_{0}$ if $S_{data} \leq 1$ .

FIGURE 2 Using Appendix Table I to find the critical value $S_{cirt}$ .
Step 3 Find the value of the test statistic. We have a left-tailed test, and so, from Table 3, our test statistic is

$S_{data} = number of plus signs = 1$

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Step 4 State the conclusion and the interpretation. The value of our test statistic is $S_{data} = 1$ , which is ≤1, so we reject $H_{0}$ . Evidence exists that the population median number of hurricane-related deaths is less than 50 per year.

NOW YOU CAN DO

Exercises 9–16.