EXAMPLE 28 Performing the test for using technology

A study reported that 1% of American Internet users who are married or in a long-term relationship met on a blind date or through a dating service.13 A survey of 500 American Internet users who are married or in a long-term relationship found 8 who met on a blind date or through a dating service. If appropriate, test whether the population proportion has increased. Use the -value method with level of significance .

Solution

We have and . Checking the normality conditions, we have

The normality conditions are met and we may proceed with the hypothesis test.

  • Step 1 State the hypotheses and the rejection rule.

    Our hypotheses are

    where represents the population proportion of American Internet users who are married or in a long-term relationship and who met on a blind date or through a dating service. We will reject if the -value # 0.05.

  • Step 2 Calculate .

    We use the instructions supplied in the Step-by-Step Technology Guide on page 552. Figure 37 shows the TI-83/84 results from the test for , Figure 38 shows the results from Minitab, and Figure 39 shows the results from CrunchIt!.

    image
    Figure 9.47: FIGURE 37 TI-83/84 results.

    549

    Note: Minitab, TI-83/84, and CrunchIt! round results to different numbers of decimal places.

    image
    Figure 9.48: FIGURE 38 Minitab results.

    We have

    which concurs with the TI-83/84 results in Figure 37.

  • Step 3 Find the -value.

    From Figures 37, 38, 39, and 40 we have

    image
    Figure 9.49: FIGURE 39 CrunchIt! results.
    image
    Figure 9.50: FIGURE 40 -Value for a right-tailed test.

  • Step 4 State the conclusion and interpretation.

    Because is , we do not reject . There is insufficient evidence that the population proportion of American Internet users who are married or in a long-term relationship and who met on a blind date or through a dating service has increased.