Question

Suppose the Census needed to be $98\%$ confident of the population mean length of time. Would the Census have to survey more people? Why or why not?

Short answer

It is not required for the census to survey a larger number of people because the level of confidence does not depend on the sample size.

Step-by-step solution

Given Information

$n=samplesize=200$

$x=Samplemean=8.2$

$\sigma =Populations\tan darddeviation=2.2$

Explanation

We are increasing the confidence level from $90\%$ to $98\%$.

However, we have not been given whether they want to keep the error bound the same or not.

If they want to keep the error bound the same, then the Census will need to survey more people (as increasing the confidence level will increases the error bound and increasing the sample size will decreases the error bound again).

If they do not want to keep the error bound the same, then the sample size doesn't need to be increased and thus we don't require more people in the survey (as the error bound will simply increase).