Introduction to MINITAB in the Saint Mary's Microcomputer Lab

VIII. t-tests and estimation on the mean of one population

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)

A: Estimation (confidence interval)

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].

 

B: Hypothesis test

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.

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Last update 8/21/00

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