The ______ the desired width of a confidence interval, the ______ the necessary sample size.

A) larger; larger
B) smaller; smaller
C) larger; smaller
D) smaller; larger

When the desired width of a confidence interval is smaller, this means we want a more precise estimate, which leads to a larger necessary sample size. Conversely, if we are willing to tolerate a larger interval width, we can obtain a smaller sample size. Therefore, the relationship is inverse, making option D the correct choice.