EXAMPLE 7 Test for : Critical-value method

Using Table 7, test whether women's population mean body temperature differs from that of men, using the critical-value method and .

Solution

Both sample sizes are large (), so we can perform the hypothesis test.

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  • Step 1 State the hypotheses.

    The key words “differs from” indicate a two-tail test:

    where and represent the population mean body temperature for women and men, respectively.

  • Step 2 Find and state the rejection rule.

    The required degrees of freedom is the smaller of and , which is . Unfortunately, is not in the table in Appendix Table D, so we use the conservative . For , this gives . We have a two-tailed test, so Table 8 gives us the following rejection rule:

  • Step 3 Find .

  • Step 4 State the conclusion and the interpretation.

    The test statistic is greater than (see Figure 11). We therefore reject . There is evidence, at level of significance , that the population mean body temperatures are not the same for women and men.

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    Figure 10.11: FIGURE 11 falls within the critical region.

NOW YOU CAN DO

Exercises 3–6.