Data Analysis with Microsoft Excel: Updated for Office 2007

238 Fundamentals of Statistics

The width of the acceptance region shrinks from 11.76 (44.12 to 55.88)

with a sample size of 25 to 8.32 (45.84 to 54.16) with a sample size of 50.

The observed sample average lies within the rejection region, so you reject

the null hypothesis with a p value of 1.84%.

Now let’s see what happens when you increase the value of s from 15 to 20.

To increase the value of s:

1 Click the Population Sigma box, and change the value from 15 to 20.

Because the value of s has increased, the value of the standard error

has increased too, from 2.121 to 2.828. The lower critical value has

fallen to 44.456 and the p value has increased to 7.71%, so you do

not reject the null hypothesis. Variability is one of the most impor-

tant factors in hypothesis testing; much of statistical analysis is con-

cerned with reducing or explaining variability.

Finally, let’s fi nd out what our conclusions would be if we used a

one-tailed test, where Ha is the hypothesis that the mean, 50.

To change to a one-tailed test:

2 Click the Ha: Mean < 50 (1-tailed) option button.

The chart changes to a one-tailed test. See Figure 6-9.

Figure 6-8

Changing

the sample

size from

25 to 50

sample

size = 50

you reject the null

hypothesis with the

increased sample size

increasing the sample size decreases the spread of

the distribution around the sample average