Data Analysis with Microsoft Excel: Updated for Office 2007

Chapter 6 Statistical Inference 239

Under a one-tailed test, we reject the null hypothesis. Of course, we have

to be very careful with this approach, because we are changing our hypoth-

esis after seeing the data. If this were an actual situation, changing the hy-

pothesis like this would be inappropriate. The better course would be to

draw another random sample of 25 batches and test the new hypothesis on

that set of data (and only if we have compelling reasons for doing a one-

tailed test).

Try other combinations of hypothesis and parameter values to see how

they affect the hypothesis test. Close the workbook when you’re fi nished.

You do not have to save your changes.

Additional Thoughts about Hypothesis Testing

One important point you should keep in mind when hypothesis testing is

that accepting the null hypothesis does not mean that the null hypothesis is

true. Rather, you are stating that there is insuffi cient reason to reject it. The

distinction is subtle but important. To state that accepting the null hypoth-

esis means that m 5 50 excludes the possibility that m actually equals 49 or

49.9 or 49.99. But you didn’t test any of these possibilities. What you did

test was whether the data are incompatible with the assumption that m 5 50.

You found that in some cases, they are not compatible.

Figure 6-9

Switching

from a

two-tailed

to a

one-tailed

test

one-tailed rejection

region