EXAMPLE 22 Estimating the -value using the table

Suppose we did not have access to technology. Estimate the -value from Example 19 using the table (Appendix Table D). For Example 19, our hypotheses are

where represents the population mean number of hours worked per week. Our test statistic is .

Solution

For a two-tailed test, choose the row of the table with the heading “Area in two tails.” Then select the row in the table with the appropriate degrees of freedom, in this case . Note the -values in this row: 1.311, 1.699, 2.045, 2.462, and 2.756. Think of these values as existing on a horizontal number line. We want to place our somewhere on this number line, but all the -values in the table are positive. Fortunately, because of the symmetry of the distribution about zero, we may take . Now, where would fit on this “number line”? Between 1.311 and 1.699, as indicated in Figure 31, an excerpt from the table. Therefore, we may estimate the -value to be between 0.20 and 0.10. In fact, the actual -value for this problem is about 0.144 (see Figure 32), so that our estimate is confirmed.

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