Biostatistics

EXERCISES 197
x 2 1 ða=2Þ ¼ 14:449 and x2 a=2
¼ 1:237. Our 95 percent confidence interval for
s 2 is
639:763 ð Þ
14:449 < s2 < 639:763 ð Þ
1:237
16:512 < s 2 < 192:868
The 95 percent confidence interval for s is
4:063 < s < 13:888
We are 95 percent confident that the parameters being estimated are within
the specified limits, because we know that in the long run, in repeated
sampling, 95 percent of intervals constructed as illustrated would include the
respective parameters.
&
Some Precautions Although this method of constructing confidence intervals for
s 2 is widely used, it is not without its drawbacks. First, the assumption of the normality of
the population from which the sample is drawn is crucial, and results may be misleading if
the assumption is ignored.
Another difficulty with these intervals results from the fact that the estimator is not in
the center of the confidence interval, as is the case with the confidence interval for m. This
is because the chi-square distribution, unlike the normal, is not symmetric. The practical
implication of this is that the method for the construction of confidence intervals for s 2 ,
which has just been described, does not yield the shortest possible confidence intervals.
Tate and Klett (12) give tables that may be used to overcome this difficulty.
EXERCISES
6.9.1. A study by Aizenberg et al. (A-23) examined the efficacy of sildenafil, a potent phosphodiesterase
inhibitor, in the treatment of elderly men with erectile dysfunction induced by antidepressant
treatment for major depressive disorder. The ages of the 10 enrollees in the study were
74; 81; 70; 70; 74; 77; 76; 70; 71; 72
Assume that the subjects in this sample constitute a simple random sample drawn from a population
of similar subjects. Construct a 95 percent confidence interval for the variance of the ages of subjects
in the population.
6.9.2. Borden et al. (A-24) performed experiments on cadaveric knees to test the effectiveness of several
meniscal repair techniques. Specimens were loaded into a servohydraulic device and tension-loaded
to failure. The biomechanical testing was performed by using a slow loading rate to simulate the
stresses that the medial meniscus might be subjected to during early rehabilitation exercises and
activities of daily living. One of the measures is the amount of displacement that occurs. Of the 12
specimens receiving the vertical mattress suture and the FasT-FIX method, the displacement values