One Sample T-Test

Before starting – one
caution. When you choose the *alternative* hypothesis for your test, you
are also choosing the type of confidence interval that Minitab reports. In
intro stats courses we confine ourselves mostly to two-sided confidence
intervals: Between L and U. To obtain the two-sided confidence interval you
must set Alternative: not equal to. This will be pointed out again, below. “Not
equal to” is the default, so if you choose only to get a confidence interval,
and ignore the inputs for tests, you will be fine.

A random sample of 6 one-bedroom apartments from a local newspaper has these monthly rents (dollars): 535, 685, 635, 540, 485, 585. Do these data give good reason to believe that the mean rent of all advertised apartments is greater than $500 per month?

So, the hypotheses are H_{0}:
m = 500 H_{A}: m > 500
where m (the greek letter “mu”) is the mean monthly rent of
all 1 bedroom apartments.

You need to:

- Get the data in a Minitab column
- Tell Minitab what column the data is in
- Tell Minitab what value is in the null hypothesis
- Tell Minitab about the direction in the alternative hypothesis

Here the data are in column C2.

The first part of the dialogue allows you to input the null value (500) as well as designate the column of data

Press Graphs if you want a Graph. But Options is required for a one-tailed test. Our alternative specifies “greater than.”

Click OK a couple times and the following shows up in the session window. Notice how Minitab “echoes” the hypotheses: It tells you what hypotheses it is testing (check against yours). Here the test statistic is T = 2.60 and the P-value is 0.024.

**One-Sample T: rent **

** **

Test of mu = 500 vs > 500

95%

Lower

Variable N Mean StDev SE Mean Bound T P

rent 6 577.500 73.058 29.826 517.399 2.60 0.024

You can see (look above) that there’s no “confidence interval” just a “lower bound.” To get the usual sort of 2-sided confidence interval (lower and upper bounds) you have to go back through the whole process again, changing the alternative to “not equal to.”

When you do so, you get the output below – the familiar confidence interval.

**One-Sample T: rent **

** **

Test of mu = 500 vs not = 500

Variable N Mean StDev SE Mean 95% CI T P

rent 6 577.500 73.058 29.826 (500.830, 654.170) 2.60 0.048