EXAMPLE 17 confidence interval for

Use the sample statistics from Example 15 to do the following:

  1. Calculate and interpret the margin of error for confidence level 99%.
  2. Construct and interpret a 99% confidence interval for .

613

Solution

The conditions for the confidence interval are the same as for the hypothesis test and were checked in Example 15.

  1. From Table 1 in Chapter 8 on page 432, the value for a 99% confidence level is 2.576. Therefore, the margin of error is

    The margin of error is 0.079, so we may estimate to within 0.079 with 99% confidence.

  2. The point estimate is . The 99% confidence interval is therefore

    We are 99% confident that the difference in population proportions of males and females who agree that technology will lead to a better future lies between 0.081 and 0.239.

NOW YOU CAN DO

Exercises 13–18.