Minitab will carry out the calculations based on the standard
normal (Z) distribution, to calculate confidence interval estimates
or perform hypothesis tests for the mean of a single variable.
You must have the **actual data** entered in one column, and
**you must already know the standard deviation of the population
**(sigma). The program will not check to see whether the calculations
are appropriate but will simply carry them out. Except for people
first learning to carry out inferences, the Z-calculations are
rarely appropriate because sigma is rarely known if the mean is
not known.

To obtain an interval estimate of a population mean with confidence
p% (a "p% confidence interval"), **if you know the
population standard deviation** (if you don't, this command
is inappropriate)**:** .

- 1. Use
**Stat>Basic Statistics>1-sample Z**. In the window that opens, the cursor will be in a panel labeled "Variable" and there will be a list of columns (=variables) in a panel at the left. - 2. With the cursor in the "Variable" box, select the column you want to use to estimate the population mean (either double-click on the name or highlight the name and click "Select").
- 3. Enter the population standard deviation in the panel for
"
**Sigma**" - 4. Click "
**Options"**, enter the desired confidence level beside**Confidence level** - 5. Click "OK" for the options
- 6. Click "OK"

The program will show (in the Session window)

- A heading - "One sample Z (variable name)"
- A line of text "The assumed sigma = [The value you entered for sigma]"
- A line of text which identifies the numbers on the next line (and states the confidence level used)
- The Variable name (column number, if you didn't name the variable), the sample size (labeled "N"), sample mean (labeled "Mean"), sample standard deviation (labeled "StDev"), standard error of the mean (sigma/sqrt(N) - labeled "SE Mean"),and the interval in the form (lower endpoint, upper endpoint) (labeled "__% C. I." - with the percent you specified filled in].

To carry out a test of the hypothesis "mean (of population) is (different from/greater than/less than) V" versus "mean is equal to V" (for a fixed number V), you can obtain the required values to give an answer at any desired level of significance.

- 1. Select
**Stat>Basic Statistics>1-sample Z** - 2. With the cursor in the "Variable" box, select the column you want to use for your decision about the population mean (either double-click on the name or highlight the name and click "Select").
- 3. Enter the population standard deviation for "Sigma"
- 4. In the box beside "Test Mean" type the number V to from your null and alternative hypotheses (replace any number that is there)
- 5. Click on "Options" and select the form of the
alternative hypothesis (greater than, less than, not equal) in
the popup menu next to "Alternative" and click "OK"
(for the Options)

6. Click "OK" again (in the main window)

The program will show (in the Session window)

- A heading "One sample Z: (variable name)"
- A statement of the test you have carrried out "Test of mu = [the number V] vs mu {">" or "<" or "not ="} [the number V]
- A line of text "The assumed sigma = [value you entered for sigma]"
- A line of text which identifies the numbers on the next line:
- the Variable name (or column number, if you failed to name it), the sample size (labeled "N"), sample mean(labeled "Mean"), (sample) standard deviation (labeled "StDev") standard error of the mean ( sigma /sqrt(N) - labeled "SE Mean"),
- Another line of text identifying another row of values:
- The variable name, the boundaries for a one-or two-sided confidence interval for the mean, the Z-value [(sample mean-hypothesis)/SE) - labeled "Z" ] (used in comparison to the critical Z-value for your rejection criterion) and the p-value ( the risk of Type I error if you reject the null with this sample - based on the data and your statement of the alternative - labeled "P-Value").

The program **will not give a yes-or-no answer**, because
you cannot enter the significance level desired. It does calculate
the Z-value for the sample (you can reject the null hypothesis
if this value is in the rejection region for the level of significance
you are using) and the p-value (you can reject the null hypothesis
if this value is less than the level of significance you are using).
If you have stated the alternative incorrectly, the p-value will
be incorrect, but the Z-value will still be correct.

Last update 8/10/00

*Maintained by cpeltier@saintmarys.edu*