Question

In the construction of confidence intervals if all other quantities are unchanged, an increase in the standard deviation will lead to a _____ interval.

a. narrower
b. wider
c. same size
d. not enough info

Answer 1

Answer: B) wider

The margin of error, abbreviated MoE, is defined as

MoE = sigma/sqrt(n)

sigma represents the population standard deviation. If you do not know sigma, then use s to approximate sigma. The variable s is the sample standard deviation.

As sigma gets larger, so does the MoE. The MoE directly determines how wide or narrow the confidence interval is. A smaller MoE means we're more confident with less error, while a larger MoE means we cast a wider net but there's more error.