statistic QAs

Hypothesis Tests and Confidence Intervals in Minitab Express

Open Minitab Express. You may enter your data as you would in Microsoft Excel (or any other

spreadsheet), or you can copy and paste the data from another application (like Excel).

Example: t-test. A student weighed ten samples of ½ of hazelnut coffee from a local coffee

house. The results, in pounds, are given in the table shown. We’ll investigate whether the

sample provides evidence that the average ½ pound of coffee is actually less than ½ pound.

Copy the data and paste it into Minitab.

A normal probability plot and the result of

an Anderson-Darling test (p = 0.5461)

suggest that t-procedures are OK to use.

Click the Statistics tab. You’ll see a large

number of options for statistical analysis.

For hypothesis tests and confidence intervals involving

1-sample, click on One-Sample

For tests about a population mean, select 1-sample t-test.

For tests about a population proportion, select 1-sample

proportion test.

For the example using weights of ½ pounds of coffee, we want

a 1-sample t-test. A dialog box will open like this:

Your data can be either summary data (mean, SD) or raw data.

Use the pull-down menu to select which you have. In this

example, we have the raw data, so select Sample data in a

column.

Weights

0.48

0.51

0.47

0.49

0.49

0.5

0.52

0.48

0.49

0.51

Highlight the column that contains the variable data and

then select that variable by clicking the arrow.

Next, check the box: Perform hypothesis test.

In the Hypothesized mean box, enter the hypothesized

mean (that’s the value you’re comparing the sample mean

to). In the example, the coffee bags should be 0.5 pounds.

Click on the Options tab. This allows you to choose the direction of the alternative hypothesis and set the

confidence interval level.

Use the pull-down menu Alternative hypothesis to pick the

direction of the alternative hypothesis. For this example, we

want Mean < hypothesized value.

Unless you have a 2-sided test, you can ignore the

Confidence level box.

In the output window, you’ll see results of the

hypothesis test.

You will see the mean, standard deviation and

standard error of the sample

Below, you find the p-value is 0.1299, so we

don’t reject the null hypothesis.

The sample doesn’t provide enough evidence to

support the claim that the average weight of ½

pound bags of this coffee is actually less than ½

pound.

Hypothesis Tests for a Population Proportion in Minitab Express

Example: proportion test. The standard treatment for a disease

works in 67.5% of all patients. A new treatment is proposed. Is it

better? A clinical trial of n = 100 randomly selected patients is

conducted in which 77 people are cured. Is the new treatment

better? Test at the 1% significance level.

Click the Statistics tab.

Click on One-Sample and then click on Proportion.

A dialog box will appear like this:

From the pull-down menu, select Summarized data.

Enter the number of events and the number of trials.

Then check the Perform hypothesis test box and enter

the hypothesized proportion.

Next, click the Options tab.

From the Alternative hypothesis pull-down

menu, select the appropriate alternative

hypothesis. In this example, the claim is that

the proportion of cures with the new

treatment will be higher, so select

Proportion > hypothesized value

For Method, use the default Exact.

Press OK.

The results of the hypothesis test appear in the output

window.

Minitab gives you a summary of the sample data.

Below the descriptive statistics you will see the results of

the hypothesis test including the p-value

Since the p-value is less than 0.05 (p = 0.0248), the

conclusion we draw from the hypothesis test is that the

proportion of cures with the new treatment is significantly

higher than 67.5%.

Confidence Interval for a Population Mean in Minitab Express

To construct a confidence interval for a mean (for example, the coffee data),

from the Statistics tab, click One Sample and select 1-sample t-test as you

did for the hypothesis test.

Again, you will see a dialog box like this:

Use the pull-down menu to select which

kind of data you have (raw data or

summaries). In this example, we have the

raw data, so select Sample data in a

column.

Since we’re not doing a hypothesis test,

leave the Perform hypothesis test box

unchecked.

Click on the Options tab. This allows you to choose the direction of the alternative hypothesis and set the

confidence interval level.

Use the pull-down menu Alternative hypothesis to

pick the direction of the alternative hypothesis.

For a confidence interval, we always want

Mean  hypothesized value.

Finally, in the Confidence level box, you can either

enter a confidence level or select from the pull-

down menu.

Click OK. The results (including the

confidence interval) will appear in

the output window.

Notice that in this case, the hypothesized mean is contained in the confidence interval. This gives

additional support to the conclusion of the hypothesis test that the average

weight of the ½ pound bags of coffee is not less than ½ pound.

Confidence Interval for a Population Proportion in Minitab Express

Click on One-Sample and then click on Proportion.

From the pull-down menu, select

Summarized data.

Enter the number of events and the

number of trials.

Leave the Perform hypothesis test

box blank

Next, click the Options tab.

Use the pull-down menu Alternative hypothesis to

pick the direction of the alternative hypothesis. For

a confidence interval, we always want Mean 

hypothesized value.

In the Confidence level box, you can either enter a

confidence level or select from the pull-down

menu.

For Method, use the default Exact.

Press OK. The results (including the confidence

interval) will appear in the output window.

So, we are 95% confident that for all people in the

population, the cure rate for the new treatment is

between 67.5% and 84.8%.

Notice that in this case, the hypothesized proportion, 0.675, is contained in the confidence interval. This

seems to contradict the hypothesis test that said the proportion of cures with the new treatment is

significantly higher than 67.5%. This phenomenon will occur when performing a 1-sided hypothesis test

for which the p-value is fairly close to the level of significance. For our example, the p-value was 0.0248

which is close to 0.05. If the p-value is small (compared to the significance level), this result will

generally not happen.