If three 90% confidence intervals for a population proportion p are calculated based on three independent samples selected randomly from the population, then the simultaneous confidence level will be
A) about 73%
B) exactly 90%
C) exactly 81%
D) exactly 270%
E) None of the above answers are correct.

Question

Quizplus · Accepted Answer

The simultaneous confidence level will be lower than any single confidence level because there is greater variability when multiple intervals are considered. One way to approximate the simultaneous confidence level is to use the Bonferroni correction, which divides the desired confidence level by the number of intervals being considered. In this case, since there are three intervals, the Bonferroni correction gives a confidence level of 0.90/3 = 0.30. To convert to a percentage, we multiply by 100 to get 30%. However, since this is the lower bound on the confidence level, we can say that the simultaneous confidence level is about 73% (which is closer to choice A than choice C).

If Three 90% Confidence Intervals for a Population Proportion P