EXAMPLE 4 Hypothesis test for slope using the critical-value method

Test whether a linear relationship exists between age and text messages, using the data from Table 1 at level of significance .

Solution

The regression assumptions were shown to be valid in Example 2. We may thus proceed with the hypothesis test.

  • Step 1 State the hypotheses.
    • No linear relationship exists between age and text messages.
    • A linear relationship exists between age and text messages.

  • Step 2 Find the critical value and the rejection rule. To find , use the distribution table (Table D in the Appendix) for a two-tailed test and degrees of freedom . The rejection rule for this two-tailed test is

    Here, , so . For level of significance , the table gives us . We will reject if .

  • Step 3 Calculate . From Example 3, we have

  • Step 4 State the conclusion and the interpretation. Because , we reject . There is evidence, at level of significance , that and that a linear relationship exists between age and text messages.

NOW YOU CAN DO

Exercises 15–18.