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 H0: m = 500 HA: 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