Data Analysis with Microsoft Excel: Updated for Office 2007

Chapter 6 Statistical Inference 231

By reducing the confi dence interval to 75%, you’ve reduced the width

of the confi dence band, but at the cost of many more red lines appearing on

your chart. If you were relying upon this confi dence interval to capture the

value of m, you would run a great risk of making an error. Let’s go the other

way and increase the confi dence interval.

To increase the size of the confi dence interval:

1 Drag the vertical scroll bar down until the value 99.0% appears in

the Confi dence Interval box.

All of the confi dence intervals now capture the value of m, but the size of

the confi dence bands has greatly increased. As you can see, there is a trade-

off in using the confi dence interval. Selecting too small a value could result

in missing the value of m. Selecting a larger value will almost certainly cap-

ture m, but at the expense of having a range of values too broad to be useful.

Statisticians have generally favored the 95% confi dence interval as a com-

promise between these two positions.

An important lesson to learn from this simulation is to not take the sample

average at face value. Confi dence intervals help you quantify how precisely

the sample average estimates the value of m. The next time you hear in the

news that a study has shown that a drug causes a mean decrease in blood

Figure 6-5
75% confidence
intervals

only 75% of the confidence

intervals capture the true mean