Question 6.48

6.48 More than one confidence interval.

As we prepare to take a sample and compute a 95% confidence interval, we know that the probability that the interval we compute will cover the parameter is 0.95. That’s the meaning of 95% confidence. If we plan to use several such intervals, however, our confidence that all of them will give correct results is less than 95%. Suppose that we plan to take independent samples each month for five months and report a 95% confidence interval for each set of data.

  1. What is the probability that all five intervals will cover the true means? This probability (expressed as a percent) is our overall confidence level for the five simultaneous statements.
  2. Suppose we wish to have an overall confidence level of 95% for the five simultaneous statements. About what confidence level should we pick for the construction of the individual intervals?