Z confidence interval and Z test
Given
and C level, Minitab can calculate
the Z confidence interval for 
on each
column separately. The interval is between
,
where the 
is the means of data, n is the
sample size and the z* is critical value from normal table
corresponding to C confidence level. When C level is not specified,
C=0.95 is used automatically by Minitab.
Use
the Example 6.4 in BPS chapter 6 to illustrate how to calculates
Z confidence interval. In this case we want to know a 99% confidence
interval for the true concentration .
First of all we enter the data in a worksheet. A small data set
of concentrations of one specimen is shown right. 
The
is known to be 0.0068 grams per liter. We need select Stat->Basic
Statistics->1-Sample Z from the menu, fill out the dialog
as shown below, Z confidence interval will be shown in session
window.
Same result can be obtained by using session command ZInterval:
MTB > ZInterval 99 .0068 'concentration'
To
address whether the mean we get from sample, with known , is equal, large or less than a certain mean
we expect, a Z test has to be performed. As in example
6.4, we wish to know if the mean concentration of the specimen
is equal to .86 or not. Select Stat->Basic Statistics->1-Sample
Z to do the hypothesis test. Fill out the dialog box as shown
below, then the Z test result appears on the session window.
Be ware to choose the desired alternative hypothesis in Alternative box .
The
smaller the P-value is, the stronger is the evidence against
H0
provided by the data. In our case, the P-value is very
small and the null hypothesis should be rejected.