A First Course in Statistics, 12th Edition

5.5 Determining the Sample Size

Recall from Section 1.5 that one way to collect the relevant data for a study used to make inferences about a population is to implement a designed (planned) experiment. Perhaps the most important design decision faced by the analyst is to determine the size of the sample. We show in this section that the appropriate sample size for making an inference about a population mean or proportion depends on the desired reliability.

Estimating a Population Mean

Consider Example 5.1 (p. 255), in which we estimated the mean length of stay for patients in a large hospital. A sample of 100 patients’ records produced the 95% confidence interval $\overline{x}\pm 1.96{\sigma }_{\overline{x}}=4.5\pm .78$. Consequently, our estimate $\overline{x}$ was within .78 day of ...