Example 6.12

EXAMPLE 6.12 How the Confidence Level Affects the Confidence Interval

Suppose that for the student credit card data in Example 6.10 (pages 307–308), we wanted 99% confidence. Table D tells us that for 99% confidence, $z^{*} = 2.576$ . The margin of error for 99% confidence based on 532 observations is

$\begin{array}{l} m & = & z^{*} \frac{σ}{\sqrt{n}} \\ = & 2.576 \frac{1130}{\sqrt{532}} \\ = & 126.20 \end{array}$

and the 99% confidence interval is

$\begin{array}{l} \bar{x} \pm m & = & 755 \pm 126 \\ = & (629, 881) \end{array}$

Requiring 99%, rather than 95%, confidence has increased the margin of error from 96 to 126. Figure 6.11 compares the two intervals.

FIGURE 6.11 Confidence intervals, Examples 6.10 and 6.12. The larger the value of

$C$ , the wider the interval.