When you compute a confidence interval on the mean, you compute the mean of a sample in order to estimate the mean of the population. Clearly, if you already knew the population mean, there would be n...When you compute a confidence interval on the mean, you compute the mean of a sample in order to estimate the mean of the population. Clearly, if you already knew the population mean, there would be no need for a confidence interval. However, to explain how confidence intervals are constructed, we are going to work backwards and begin by assuming characteristics of the population. Then we will show how sample data can be used to construct a confidence interval.
We begin with testing hypotheses about the population mean. Just like our considerations of confidence intervals for means, we will have two cases to consider based on whether the population standard ...We begin with testing hypotheses about the population mean. Just like our considerations of confidence intervals for means, we will have two cases to consider based on whether the population standard deviation is known or unknown. The latter case is the more frequently occurring case as we discussed in the chapter on confidence intervals, but we again begin with the case that the population standard deviation is known because of pedagogical considerations.