Q. 24 - The Practice of Statistics for AP

Question

A polling organization announces that the proportion of American voters who favor congressional term limits is  $64\%$, with a $95\%$ confidence margin of error of $3\%$. If the opinion poll had announced the margin of error for 80% confidence rather than $95\%$ confidence, this margin of error would be

(a) $3\%$, because the same sample is used.

(b) less than $3\%$, because we require less confidence.

(c) less than $3\%$, because the sample size is smaller.

(d) greater than $3\%$, because we require less confidence.

(e) greater than $3\%$, because the sample size is smaller. 

Step-by-Step Solution

Answer

(b) less than $3\%$, because we require less confidence

Step 1: Given Information

(a) $3\%$, because the same sample is used.

(b) less than $3\%$, because we require less confidence.

(c) less than $3\%$, because the sample size is smaller.

(d) greater than $3\%$, because we require less confidence.

(e) greater than $3\%$, because the sample size is smaller. 

Step 2: Explanation

The confidence level is decreased from $95\%$ to $80\%$. This would then mean that the confidence interval becomes less accurate, that is, we require less confidence/accuracy and thus the confidence interval also becomes less wide.

If the confidence interval becomes less wide, then the margin of error decreases, and thus the margin of error will be less than $3\%$.