Why Is It Necessary to Adjust the Individual Confidence Level

Multiple Choice

Why is it necessary to adjust the individual confidence level of each confidence interval for a multiple comparison of means procedure?

A) The total probability of the intervals being correct will always be less than the probability of any single confidence interval covering a single mean difference.
B) Each confidence interval is slightly biased and the correction will alleviate that bias.
C) The intervals will not be able to detect slight differences in means without a correction.
D) Confidence intervals are always estimates; so, when considering of them, an adjustment is needed to allow for valid inference.