Data Analysis with Microsoft Excel: Updated for Office 2007

Chapter 6 Statistical Inference 257

where m 1 is the assumed mean of the fi rst distribution and m 2 is the mean
of the second distribution. Notice that we are not making any assumptions
about what the actual values of m 1 and m 2 are; we are interested only in the
difference between them. Because the standard deviations of the two sam-
ples are close in value, we’ll use a pooled t test to test the null hypothesis.
First, we must calculate the value of the pooled standard deviation, s:

s 5

Å

(^1) n 1212 s^2111 n 2212 s^22
n 11 n 222

5

Å

12521282112521262

2512522

5 7. 07

Thus, the t statistic equals

t 5

(^1) x 12 x 2221 m 1 2m 22
s
Å

1

n 1

1

1

n 2

5

(^175280220)

7.07

Å

1

25

1

1

25

522 .5

which should follow a t distribution with 48 degrees of freedom. Is this a
signifi cant value?

To evaluate the t statistic:

1 Open a blank workbook. In cell A1 type =TDIST(2.5,48,2) and press
Enter.
Note that we enter the value 2.5 rather than 22 .5 because the TDIST
function works with positive values. We enter the value 2 as the
third parameter because this is a two-sided test.

Excel returns a p value of 0.016, and we reject the null hypothesis. We
conclude that the evidence supports the conclusion that students learn bet-
ter how to write using the new teaching method.