Coleman surveys a random sample of city residents and uses a 95% confidence interval to estimate the proportion of all city residents who plan to vote in an upcoming election. Emma isn't satisfied with 95% confidence. She wants to use a 99% confidence interval, but she doesn't want it to be any wider that Coleman's 95% confidence interval. In order to achieve this, Emma must
A) take a sufficiently larger random sample of city residents.
B) take a sufficiently smaller random sample of city residents.
C) reject the null hypothesis.
D) have a sufficiently small P-value.
E) Both reject the null hypothesis, and have a sufficiently small P-value.

Question

Quizplus · Accepted Answer

In order to increase the confidence level while keeping the width of the confidence interval the same, we need to increase the sample size. This is because a larger sample size will result in a smaller standard error, which will allow us to have a narrower confidence interval at a higher confidence level. Therefore, Emma must take a sufficiently larger random sample of city residents.

Coleman Surveys a Random Sample of City Residents and Uses