In this chapter we discussed confidence intervals for population means, proportions, and totals. We began by assuming that the population is either infinite or much larger than (say, at least 20 times as large as) the sample. First, we studied how to compute a confidence interval for a population mean. We saw that when the population standard deviation <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0072977477/302316/sigma.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> is known, we can use the normal distribution to compute a confidence interval for a population mean. When <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0072977477/302316/sigma.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> is not known, if the population is normally distributed (or at least mound-shaped) or if the sample size n is large, we use the t distribution to compute this interval. We also studied how to find the size of the sample needed if we wish to compute a confidence interval for a mean with a prespecified confidence level and with a prespecified margin of error. Figure 7.20 is a flowchart summarizing our discussions concerning how to compute an appropriate confidence interval for a population mean.

Next we saw that we are often interested in estimating the proportion of population units falling into a category of interest. We showed how to compute a large sample confidence interval for a population proportion, and we saw how to find the sample size needed to estimate a population proportion with a prespecified confidence level and with a prespecified margin of error.

In optional Section 7.5 we continued by studying how to compute confidence intervals for parameters of finite populations that are not much larger than the sample. We saw how to compute confidence intervals for a population mean and total when we are sampling without replacement. We also saw how to compute confidence intervals for a population proportion and for the total number of units in a category when sampling a finite population. In optional Section 7.6 we concluded this chapter by comparing confidence intervals with tolerance intervals.