confidence interval that goes from 42 mpg to plus infinity mpg!

In biostatistics, it is traditional to always use two-way CIs rather than one-way CIs, as these

are seen as most conservative.

Calculating Confidence Intervals

Although an SE and a CI are different calculations intended to express different information, they are

related in that the SE is used in the CI calculation. SEs and CIs are calculated using different formulas

(depending on the type of sample statistic for which you are calculating the SE and CI). In the

following sections, we describe methods of calculating SEs and CIs for commonly used sample

statistics.

Before you begin: Formulas for confidence limits in large samples

Most of the methods we describe in the following sections are based on the assumption that your

sample statistic has a sampling distribution that’s approximately normal (Chapter 3 covers sampling

distributions). There are strong theoretical reasons to assume a normal or nearly normal sampling

distribution if you draw a large enough samples.

For any normally distributed sample statistic, the lower and upper confidence limits can be

calculated from the observed value of the statistic (V) and standard error (SE) of the statistic:

As you can see, CI calculations include a k x SE component, which is both added to and

subtracted from the estimate to get the limits. This component is called the margin of error (ME).

Confidence limits computed this way are often referred to as normal-based, asymptotic, or central-

limit-theorem (CLT) confidence limits. The value of k in the formulas depends on the desired

confidence level and can be obtained from a table of critical values for the normal distribution. Table

10-1 lists the k values for some commonly used confidence levels.

TABLE 10-1 Multipliers for Normal-Based Confidence Intervals

Confidence Level Tail Probability k Value

50%

0.50

0.67

80%

0.20

1.28

90%

0.10

1.64