Minitab will carry out the calculations, using Student's t
distribution, to perform confidence interval estimates or hypothesis
tests for the mean of a single variable. You must have the **actual
data** entered in one column. The program will not check to
see whether the calculations are appropriate but will simply carry
them out (It is up to you to check on the requirements for use
of the t-methods)

**Procedure** to obtain an interval estimate of a population
mean with confidence p% (a "p% confidence interval"):

- 1. Use
**Stat>Basic Statistics>1-sample t**. 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. Click "
**Options"**, enter the desired confidence level beside**Confidence level** - 4. Click "OK" for the options
- 5. Click "OK"

**Output **in the Session window

- A heading - "One sample T: (variable name)"
- 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].

**Procedure** 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).

- 1. Select
**Stat>Basic Statistics>1-sample t** - 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. In the box beside "Test Mean" type the number V to from your null and alternative hypotheses (replace any number that is there)
- 4. 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)

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

**Output **in the Session window

- A heading "One sample T: (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 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 t-value [(sample mean-hypothesis)/SE) - labeled "Z" ] (used in comparison to the critical t-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 t-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 t-value will
still be correct, but the p-value will be incorrect.

Last update 8/21/00

*Maintained by cpeltier@saintmarys.edu*