EXAMPLE 7.5

Estimating the mean monthly return. The mean monthly return on the client’s portfolio was %, and the standard deviation was %. Figure 7.7 gives Minitab output, and Figure 7.8 gives Excel and JMP outputs for a 95% confidence interval for the population mean . Note that Excel gives the margin of error next to the label “Confidence Level(95.0%)” rather than the actual confidence interval. We see that the 95% confidence interval is (−3.04, 0.84), or (from Excel) −1.0997 ± 1.9420.

Because the S&P 500 return, 0.95%, falls outside this interval, we know that differs significantly from 0.95% at the level. Example 7.4 gave the actual P-value as .