EXAMPLE 21 Rank correlation test: Large-sample case

Expand the previous example from countries to a random sample of countries, and conduct the same hypothesis test, using the same level of significance . Assume that the 37 countries yield a test statistic of .

Solution

The expanded data set comes from a random sample, so we proceed with the hypothesis test.

  • Step 1 State the hypotheses.

  • Step 2 Find the critical value and state the rejection rule. There are now countries, so we apply the large-sample case . With level of significance , we find our critical value from Table 16:

    We will reject if or if .

  • Step 3 Find the value of the test statistic . We use the instructions provided in the Step-by-Step Technology Guide at the end of this section. Figure 23 shows the Minitab results, with denoted as “.” Although Minitab thus identifies the statistic as the linear correlation coefficient for numerical data that we learned in Chapter 4, this statistic is nevertheless equal to the rank correlation coefficient, because it is based on ranks.
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    Figure 14.23: FIGURE 23 Minitab results.
  • Step 4 State the conclusion and the interpretation. Because , we reject , just as we did for the small-sample case. There is evidence for a rank correlation between female literacy and fertility.