A bank branch wants to estimate the average wait time in the teller line. Times from 40 randomly selected customers are recorded. What is the appropriate inference procedure?

A bank branch wants to estimate the average wait time in the teller line. Times from 40 randomly selected customers are recorded. What is the appropriate inference procedure?

• A. One-Sample T-Interval
• B. Two-Sample T-Interval
• C. Proportion Z-Test
• D. Matched-Pairs T-Test

Answer: (A)

Estimating a population mean from a single sample with unknown population standard deviation uses a one-sample t-interval. Here, the bank records wait times from 40 randomly selected customers to infer the average wait time across all customers. Because the population standard deviation isn’t known, we replace it with the sample standard deviation and use the t distribution, which accounts for extra uncertainty. With 40 observations, the sampling distribution of the mean is well-approximated by normal, and the t-interval with 39 degrees of freedom provides a reliable confidence interval for the true mean. The other approaches aren’t appropriate here: there’s only one group and we’re estimating a mean, not a proportion, and there’s no pairing to compare.

Estimating a population mean from a single sample with unknown population standard deviation uses a one-sample t-interval. Here, the bank records wait times from 40 randomly selected customers to infer the average wait time across all customers. Because the population standard deviation isn’t known, we replace it with the sample standard deviation and use the t distribution, which accounts for extra uncertainty. With 40 observations, the sampling distribution of the mean is well-approximated by normal, and the t-interval with 39 degrees of freedom provides a reliable confidence interval for the true mean. The other approaches aren’t appropriate here: there’s only one group and we’re estimating a mean, not a proportion, and there’s no pairing to compare.