EXAMPLE 13 Two-sample test

A Kaiser Family Foundation report found that the mean amount of time that young people ages 8–18 spend talking on their cell phones is minutes per day, whereas the mean amount of time spent watching TV shows on their cell phones is minutes per day.9 Assume that the sample sizes are and , and that the population standard deviations are known to be minutes and minutes. Test, using the critical-value method and level of significance , whether the population mean amount of time young people spending talking on their cell phones is less than the population mean amount of time they spend watching TV shows on their cell phones.

Solution

  • Step 1 State the hypotheses.

    where and represent the population mean amount of time young people spend talking and watching TV shows, respectively, on their cell phones.

    599

  • Step 2 Find .

    From Table 4 in Chapter 9 (page 500), we have . Reject if .

  • Step 3 Calculate .

    The test statistic for the test for takes the form

  • Step 4 Conclusion and interpretation.

    The test statistic is less than the critical value . Therefore, we reject . There is evidence that the population mean amount of time young people spending talking on their cell phones is less than the population mean amount of time they spend watching TV shows on their cell phones.

NOW YOU CAN DO

Exercises 25 and 26.