Chapter 9, Problem 66CR

The confidence intervals presented in this chapter give both lower and upper bounds on plausible values for the population characteristic being estimated. In some instances, only an upper bound or only a lower bound is appropriate. Using the same reasoning that gave the large sample interval in Section 9.3, we can say that when n is large, 99% of all samples have

$\mu <\bar{x}+2.33\frac{s}{\sqrt{n}}$

(because the area under the z curve to the left of 2.33 is 0.99). Thus, $\bar{x}+2.33\frac{s}{\sqrt{n}}$ is a 99% upper confidence bound for μ. For a sample of 539 patients waiting for bypass surgery, the mean wait time was 19 days and the standard deviation was 10 days. Calculate the 99% upper confidence bound for the population mean wait time for bypass patients.