ABSTRACT
Consider the random sample of 27 female student heights recorded in Table 1.1. These heights are represented graphically in part of Fig. 3.10, reproduced here as Fig. 9-1.
By calculation we find that the sample mean height is x = 163.4 cm, but what is our estimate of the population mean height ju l (i.e., of all first-year female students in U.K. universities)? The obvious answer is 163-4 cm, if we require a single-value estimate (often referred to as a p oint estimate). However, since our estimate is based on a sample of the population of heights, we might want to be more guarded and give some idea of the precision of the estimate by adding and subtracting an ‘e r ro r ’ te rm which might, for example, lead to a statement that our estimate is 163.4 ± 1, meaning that the population mean height lies between 162.4 and 164.4 cm. Such an estimate is referred to as an in terval estimate. Statistical theory indicates that the size of the error term and hence the w idth of the interval, depend on
00 0 0 0 0000 00
150 155 160 165 170 175 180 185 190
three factors:
1. The sam ple size, n — the larger the sample size, the smaller the error term and the smaller the width of the interval (other things being equal).
