A First Course in Statistics, 12th Edition

5.2 Confidence Interval for a Population Mean: Normal (z) Statistic

Suppose a large hospital wants to estimate the average length of time patients remain in the hospital. Hence, the hospital’s target parameter is the population mean $\mu .$ To accomplish this objective, the hospital administrators plan to randomly sample 100 of all previous patients’ records and to use the sample mean $\overline{x}$ of the lengths of stay to estimate $\mu ,$ the mean of all patients’ visits. The sample mean $\overline{x}$ represents a point estimator of the population mean $\mu$. How can we assess the accuracy of this large-sample point estimator?

According to the Central Limit Theorem, the sampling distribution of the sample mean is approximately normal for large samples, as shown in ...