Introduction to MINITAB in the Saint Mary's Microcomputer
Lab
XI. Inference on a proportion
Hypothesis tests and Confidence Interval calculations are carried
out with the same command, but inferences on a single propotion
or on the difference of two proportions require differenct commands.
Minitab will not check whether the conditions for using the test
are met but will simply carry out the calculations. Checking appropriatness
is your job.
Minitab will perform tests or calculate confidence intervals
for proportions either from Summarized data (you enter
the sample size/number of trials and the number of successes for
each sample) or from raw data (Data in a column of 1's
- each representing a success - and 0's - each representing a
failure).
Procedure
To calculate a confidence interval estimate for a proportion
in one population or to perform a significance test on a hypothesis
about a single proportion. Some steps will vary, depending on
how you enter the data.
- 1. Select Stat>Basic Statistics>1Proportion
- 2. If the data are in a column of 0's and 1's (raw data)
click the button (circle) next to the words "Samples
in columns", click in the panel below the words (to put
the cursor there) and select the column containing the data (by
highlighting its name and clicking "Select" - or by
double-clicking the name)
If you will be entering summary data (n and number of successes)
click the button next to "Summarized data", click in
the "Number of trials" panel and enter the number of
trials (n), click in the "Number of successes" panel
and type in the number of successes.
- 3. Click "Options" to set the confidence
level or the null and alternative hypothesis
- 4. If you want a confidence interval for the proportion of
successes, type in the confidence level in the "Level"
box and make sure the "Alternative" is set to "not
equal"
- 5. If you want to perform a test on proportion: select
the alternative hypothesis ("less than" "not equal"
or "greater than" in the "Alternative" box
and enter the proportion from the null and alternative hypothesis
in the "Test proportion" box.
- 6. If you want to use the Z-calculations for the test
and the confidence interval (np, n(1-p) large enough) check
the box "Use test and interval based on normal distribution".
Otherwise, the calculations will be based on (exact) calculations
using the binomial distribution [If the z-methods are, in fact,
legitimate, the results will be close, but not identical]
- 7. Click "OK" for the "options"
window and "OK" for the "1proportion"
window
Output in the Session window:
- A heading "Test and CI for one proportion"
- A statement of the test you have carrried out "Test
of p = [value from hypothesis] vs mu {">" or "<"
or "not ="} [value from hypothesis]
- If you had the data in a column there will be a statement
"Success = 1" to remind you which value has been read
as "success"
- A line of text which identifies the numbers on the next line:
- the Variable name (or column number, if you failed to name
it) or "1" (as the "Sample") if you entered
summary data, the sample size (labeled "N"), sample
proportion (labeled "Sample p"), the bounds for a confidence
inteval with the confidence level you stated (If you have performed
a 1-sided test, you will have a "C% upper [or lower] bound"
- the C% confidence cutoff for the propotion to be no more than
[or no less than] this value - end of a one-sided confidence
interval), 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 printout does not give a yes or no answer for the test
- you must determine that, based on the p-value and your decision
criteria.
Last update 11/27/2000
Maintained by cpeltier@saintmarys.edu