A summary function applied to a finite population vector produces a parameter. A summary function applied to a sample vector produces a statistic, or point estimate.

A point estimate may be unbiased, but it is rarely the correct value. The distribution of the point estimate allows us to create an interval which contains the true value of a parameter with a degree of confidence. The operator confInt modifies a summary function to produce a 2-item vector consisting of the lower bound and upper bound of a confidence interval.

The left argument is the confidence level; it is optional--the default is a 95%. The left operand is a summary function, typically: mean, proportion, variance or sdev. The right operand can be either a numeric vector, a 2-column matrix representing a frequency distribution, or a namespace containing count, mean and variance.

The syntax of the confInt operator is:

[*ConfLevel|*__ 0.95__] summaryFunction

Some examples follow:

A sample of 15 heights of college students was taken and is listed below:

** Height←69 69 63 63 66 67 73 67 70 72 71 63 68 63 66**

Find a 95% confidence interval for the mean height.

** mean confInt Height
65.465 69.202**

Find a 90% confidence interval for the proportion of students taller than 70 inches:

** 0.90 proportion confInt Height > 70
0.05685 0.43978**

Find a 99% confidence interval for the standard deviation.

** 0.99 sdev confInt Height
2.2555 6.2533**

Find an 80% confidence interval for the median.

** 0.8 median confInt Height
66 69**

A sample of 85 home sales from a certain city was taken and the average price was $149,000 with a standard devation of $25,000. Find a 95% confidence interval for average home price.

** mean confInt stats 85 149000 25000
143608 154392**

A sample of 38 students were asked how many siblings each had. 2 were only children, 17 had one sibiling, 11 had two siblings, 7 and three and one had four. Find a 90% confidence interval for the average number of siblings. ** **

** FD←0 1 2 3 4,[1.5]2 17 11 7 1
0.90 mean confInt FD
1.4288 1.9396**

What is a 95% confidence interval for the variance?

**0.95 var confInt FD
0.05786 1.4571 **