EXAMPLE 8 test for independence using the p-value method and technology

youngliving

The National Center for Health Statistics publishes information on the living arrangements of America's young people. Table 9 contains a random sample of 200 young people ages 1-24, indicating their gender and living arrangements. Test whether gender and living arrangement are independent, using the TI-83/84, Minitab, JMP, the p-value method, and level of significance .

Table 11.24: Table 9 Contingency table of living arrangements versus gender
Living arrangements
Gender Living with
parents		 Living with
partner		 All other
arrangements		 Total
Female 51 22 28 101
Male 58 14 27 99
Total 109 36 55 200

651

Solution

  • Step 1 State the hypotheses and the rejection rule. Check the conditions.

    • .
    • .

    Reject if the p-value .

    Note that Minitab provides the expected counts (frequencies) below the observed counts. We can then verify that none of the expected frequencies is less than 1, and that none of the expected frequencies has a value less than 5.

  • Step 2 Calculate . We use the instructions found in the Step-by-Step Technology Guide at the end of this section. The TI-83/84 results in Figure 17 tell us that . The Minitab results in Figure 18 round this to The JMP results in Figure 19 (“Pearson”) also round this to .

    image
    Figure 11.18: FIGURE 17 TI-83/84 results.
    image
    Figure 11.19: FIGURE 18 Minitab results.
    image
    Figure 11.20: FIGURE 19 JMP results.

  • Step 3 Find the p-value. From the TI-83/84 results in Figure 17, we have

  • Step 4 State the conclusion and the interpretation. Because p-value ≈ 0.329 is not less than level of significance 0.10, we do not reject There is insufficient evidence that gender and living arrangements are dependent.

NOW YOU CAN DO

Exercises 15–18.