# Computing Confidence Intervals

Suppose that the 20 people in our study are a sample of a larger population. We might desire to infer things about the larger population from the sample. We might wish to estimate what the mean of the improvement would be if the whole population had taken these tests rather than our sample. Usually this estimate is presented as a range rather than an exact number. This range is called a confidence interval.

The TINTERVAL command in MINITAB computes confidence intervals for the mean on a column of data. This interval goes from:

mean(column) - t*(s/(sqrt(n))

to:

mean(column) + t*(x/(sqrt(n))

where s is the sample standard deviation, n is the sample size, and t is the value from the t table corresponding to the percent confidence desired and (n-1) degrees of freedom. The syntax of the command is:

TINTERVAL confidencepercent column

The following example computes a 95% confidence interval for the data in the column C6, the column where we calculated the improvement from test 1 to test 4.

MTB> TINTERVAL 95 C6

N MEAN STDEV SE MEAN 95.0 PERCENT C.I.
IMPROV 20 2.90 14.56 3.26 ( -3.92, 9.72)

Note that if a confidence interval of an improvement in test scores includes the value 0, a T-Test on the same data at the same confidence interval will show that we cannot conclude that there has been any improvement. Here the confidence interval goes from -3.92 to 9.72. We would say that we are 95% sure that the true mean of the improvement from test 1 to test 4 was between -3.92 and 9.72.