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1. Often it is more convenient to specify directly the width of confidence intervals for the population mean rather than oz. This is easily accom- plished, since, for example, a 95% confidence interval for the popula- tion mean will extend approximately 1.960 on each side of the sample mean. 2. If the object of interest is the population total, the variance of the sample estimator of this quantity is No, and a 95% confidence interval for it extends approximately 1.96No on each side of NI. An obvious difficulty with the practical use of Equation 7.23 is that it involves the population variance, o, which typically will be unknown. However, often an investigator will have a rough idea of the value of this quantity. Sometimes the population variance can be estimated from a preliminary sample of the population or approximated from his- torical data mation: Single Population Example 7.15 Mortgages (Sample Size) As in Example 7.8, suppose that in a city last year, 1,118 mortgages were taken out and that a simple random sample is to be taken in order to estimate the mean amount of these mortgages. From previous experience of such populations it is estimated that the population standard deviation is approximately $20,000. A 95% confidence interval for the population mean must extend $4,000 on each side of the sample mean. How many