EXAMPLE 20 Performing the rank correlation test

Use the data in Example 19 to test whether a rank correlation exists between female literacy and fertility. Use level of significance .

Solution

The data come from a random sample, so we may proceed with the hypothesis test.

  • Step 1 State the hypotheses.
  • Step 2 Find the critical value and state the rejection rule. There are countries in the data set in Table 15, so we apply the small-sample case (). Use Appendix Table K. We select the column with level of significance and the row with . Our critical value is (see Figure 22). We will reject , if or if .
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    Figure 14.22: FIGURE 22 Finding the critical value for the rank correlation test.
  • Step 3 Find the value of the test statistic . In Example 19, we found .
  • Step 4 State the conclusion and the interpretation. Because , our conclusion is to reject . There is evidence for a rank correlation between female literacy and fertility. Because is negative, the association between female literacy and fertility is a negative relationship. That is, as female literacy increases, fertility tends to decrease, and vice versa.

NOW YOU CAN DO

Exercises 13–20.