Problem
A trade magazine routinely checks the drive-through service times of fast-food restaurants. An $80 \%$ confidence interval that results from examining 669 customers in one fast-food chain's drive-through has a lower bound of 168.5 seconds and an upper bound of 171.9 seconds. What does this mean? Choose the correct answer below. A. The mean drive through service time of this fast-food chain is 170.2 seconds $80 \%$ of the time. B. One can be $80 \%$ confident that the mean drive-through service time of this fast-food chain is between 168.5 seconds and 171.9 seconds. C. One can be $80 \%$ confident that the mean drive-through service time of this fast-food chain is 170.2 seconds. D. There is an $80 \%$ probability that the mean drive-through service time of this fast-food chain is between 168.5 seconds and 171.9 seconds.
Solution
Step 1 ：A confidence interval is a range of values, derived from a statistical calculation, that is likely to contain the value of an unknown parameter. In this case, the parameter is the mean drive-through service time.
Step 2 ：The confidence level of $80 \%$ means that if we were to repeat this process many times, we would expect the true mean to fall within this interval $80 \%$ of the time.
Step 3 ：Therefore, we can be $80 \%$ confident that the mean drive-through service time is between 168.5 seconds and 171.9 seconds.
Step 4 ：\(\boxed{\text{The correct answer is B. One can be } 80 \% \text{ confident that the mean drive-through service time of this fast-food chain is between 168.5 seconds and 171.9 seconds.}}\)
