t

The upper confidence limit (UCL) is given by T UCL = 1 + 22 (7.4) The lower confidence limit (LCL) is given by LCL = {- #a2V (7.5) We need to interpret accurately confidence intervals. If random samples of n obser- vations are drawn repeatedly and independently from the population and 100(1 - a)% confidence intervals are calculated by Equation 7.1, then over a very large number of repeated trials, 1001 - a)% of these intervals will contain the true value of the popula- tion mean. For selected confidence levels, Table 7.2 lists corresponding values of 2./2, sometimes called the reliability factor. For a 90% confidence interval, Equation 7.1 becomes the following: F 1.6450 V 2 Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known 273 ys Table 7.2 Selected Confidence Levels and Corresponding Values of 2/2 CONFIDENCE LEVEL 95% 98% 90% 0.100 a 0.05 0.02 99% 0.01 2.58 2a/2 1.645 1.96 2.33 For a 95% confidence interval, Equation 7.1 becomes the following: T + 1.96 Vn Example 7.3 Time at the Grocery Store (Confidence Interval) Suppose that shopping times for customers at a local mall are normally distributed with known population standard deviation of 20 minutes. A random sample of 64 shoppers in the local grocery store had a mean time of 75 minutes. Find the standard error, mar- gin of error, and the upper and lower confidence limits of a 95% confidence interval for the population mean, M