EXAMPLE 19 Test for using critical-value method: two-tailed test

CNN reported in 2014 that, even after factoring in part-time jobs, Americans worked an average of 38 hours per week. Suppose a social science researcher disputes this finding and is interested in testing whether the population mean number of hours worked per week differs from 38. A random sample of working Americans yields a sample mean of hours worked, with a sample standard deviation of hours. If the conditions are met, perform the appropriate hypothesis test using level of significance .

Solution

Because , we may proceed with the test.

  • Step 1 State the hypotheses.

    The key words “differs from” indicate a two-tailed test, with , because we are testing whether differs from 38. So our hypotheses are

    where represents the population mean number of hours worked per week.

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    Figure 9.26: FIGURE 21 Critical region for two-tailed test.

  • Step 2 Find and state the rejection rule.

    To find for a two-tailed test with level of significance , we look in the 0.10 column in the “Area in two tails” section of Table D in the Appendix. The degrees of freedom gives us . From Table 8, the rejection rule is: “Reject if or .”

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  • Step 3 Calculate :

  • Step 4 State the conclusion and the interpretation.

    is not ≥1.699 and it is not ≤−1.699; therefore, we do not reject . See Figure 21. There is insufficient evidence, at level of significance , that the population mean number of hours worked per week differs from 38.

NOW YOU CAN DO

Exercises 9–14.