Data Analysis with Microsoft Excel: Updated for Office 2007

Chapter 6 Statistical Inference 227

We can use a two-sided z value to construct a general expression for the

confi dence interval. The more general expression is

P ax 2 z 12 a/ 2

s

!n

,m,x 1 z 12 a/ 2

s

!n

b 512 a

Thus the upper and lower confi dence limits for m are x 6 z 12 a/ 2 s/!n. For

example, if a5 0. 0 5, then z 12 0.05/ 25 1. 96 and the 95% confi dence limits

are x 6 1.963s/!n, which is pretty close to our rule-of-thumb estimate of

62 standard errors from the sample average. Table 6-1 shows confi dence

intervals of various sizes using this approach.

Table 6-1 Confi dence Intervals

1 2 a z 1 2a/ 2 Confi dence Band

0.800 1.282 x 6 1.282 3 s/!n

0.900 1.645 x 6 1.6453s/!n

0.950 1.960 x 6 1.9603s/!n

0.990 2.576 x 6 2.576 3 s/!n

0.999 3.290 x 6 3.2903s/!n

Figure 6-2

Two-sided

z values

z0.975 = 1.96

– z0.975 (^) = – 1.96