EXAMPLE 18 Using a interval for to perform tests about

This example asks whether differs from (or is not equal to) a certain value, so we can use the confidence interval to test the hypotheses. Example 17 provided a 99% confidence interval for , the difference in population proportions of males and females who agree that technology will lead to a better future, as (0.081, 0.239). Test, using level of significance , whether the differs from these values: (a) 0.1, (b) 0.2, (c) 0.3.

Solution

  1. versus .

    The hypothesized value 0.1 lies outside the interval (0.081, 0.239), so we reject .

  2. versus .

    The hypothesized value 0.2 lies inside the interval, so we do not reject .

  3. versus .

    The hypothesized value 0.3 lies outside the interval, so we reject .

NOW YOU CAN DO

Exercises 19–22.