Example 4.9 Computing Confidence Limits for the Mean, Standard Deviation, and Variance

This example illustrates how to compute confidence limits for the mean, standard deviation, and variance of a population. A researcher is studying the heights of a certain population of adult females. She has collected a random sample of heights of 75 females, which are saved in the data set Heights:

data Heights;
   label Height = 'Height (in)';
   input Height @@;
   datalines;
64.1 60.9 64.1 64.7 66.7 65.0 63.7 67.4 64.9 63.7
64.0 67.5 62.8 63.9 65.9 62.3 64.1 60.6 68.6 68.6
63.7 63.0 64.7 68.2 66.7 62.8 64.0 64.1 62.1 62.9
62.7 60.9 61.6 64.6 65.7 66.6 66.7 66.0 68.5 64.4
60.5 63.0 60.0 61.6 64.3 60.2 63.5 64.7 66.0 65.1
63.6 62.0 63.6 65.8 66.0 65.4 63.5 66.3 66.2 67.5
65.8 63.1 65.8 64.4 64.0 64.9 65.7 61.0 64.1 65.5
68.6 66.6 65.7 65.1 70.0
;
run;

The following statements produce confidence limits for the mean, standard deviation, and variance of the population of heights:

title 'Analysis of Female Heights';
ods select BasicIntervals;
proc univariate data=Heights cibasic;
   var Height;
run;

The CIBASIC option requests confidence limits for the mean, standard deviation, and variance. For example, Output 4.9.1 shows that the 95% confidence interval for the population mean is . The ODS SELECT statement restricts the output to the "BasicIntervals" table; see the section ODS Table Names.

The confidence limits in Output 4.9.1 assume that the heights are normally distributed, so you should check this assumption before using these confidence limits. See the section Shapiro-Wilk Statistic for information about the Shapiro-Wilk test for normality in PROC UNIVARIATE. See Example 4.19 for an example that uses the test for normality.