The Essentials of Biostatistics for Physicians, Nurses, and Clinicians

64 CHAPTER 5 Estimating Means and Proportions

Figure 5.3. Explanation of 95% confi dence interval, taken from Chernick and Friis
( 2003 ), fi gure 8.2, p. 156 with permission.

Sample

0.44 0.46 0.48 0.50 0.52 0.54 0.56

95% Confidence Intervals for p

A one - sided confi dence interval will either be an interval of the
form [ a , ∞ ) or ( − ∞ , b ]. These come about most often when looking at
the difference of two parameters, such as arithmetic means for one
group versus another. Suppose group 2 has mean greater than group 1,
that is, μ 1 − μ 2 < 0. Let X be the sample mean for group 1, and let Y
be the sample mean for group 2. Then we construct a confi dence inter-
val for μ 1 − μ 2 of the form ( − ∞ , b ] with say a 95% confi dence level.
Then, in repeating this process many times, 95% of the time, the true