For Exercises 6.23 to 6.25, see page 304; for 6.26 and 6.27, see pages 305–306; for 6.28 to 6.30, see page 309; for 6.31 and 6.32, see page 311; and for 6.33, see page 313.

Question 6.27

6.27 80% confidence intervals.

The idea of an 80% confidence interval is that the interval captures the true parameter value in 80% of all samples. That’s not high enough confidence for practical use, but 80% hits and 20% misses make it easy to see how a confidence interval behaves in repeated samples from the same population.

  1. Set the confidence level in the Confidence Interval applet to 80%. Click “Sample 25” to choose 25 SRSs and display their confidence intervals. How many of the 25 intervals contain the true mean ? What proportion contain the true mean?
  2. We can’t determine whether a new SRS will result in an interval that contains or not. The confidence level only tells us what percent will contain in the long run. Click “Sample 25” again to get the confidence intervals from 50 SRSs. What proportion hit? Keep clicking “Sample 25” and record the proportion of hits among 100, 200, 300, 400, and 500 SRSs. As the number of samples increases, we expect the percent of captures to get closer to the confidence level, 80%. Do you find this pattern in your results?