Data Analysis with Microsoft Excel: Updated for Office 2007

Chapter 6 Statistical Inference 255

conclude that there has been an increase in the percentage of women par-

ticipating in the workforce during the four-year period from 1968 to 1972.

To complete your work:

1 Save your changes to the Labor Analysis workbook and close the fi le.

The Two-Sample t Test

In the one-sample or paired t test, you compared the sample average to a

fi xed value specifi ed in the null hypothesis. In a two-sample t test, you com-

pare the averages from two independent samples to determine whether a

signifi cant difference exists between the samples. For example, one sample

might contain the cholesterol levels of patients taking a standard drug, while

the second sample contains cholesterol data on patients taking an experi-

mental drug. You would test to see whether there is a statistically signifi cant

difference between the two sample averages.

To compare the sample averages from normally distributed data, you have

a choice of two t tests. One test statistic, called the unpooled two-sample

t statistic, has the form

t 5

(^1) x 12 x 2221 m 1 2m 22

Å

S^21

n 1

1

S^22

n 2

where x 1 and x 2 are the sample averages for the fi rst and second samples, s 1

and s 2 are the sample standard deviations, n 1 and n 2 are the sample sizes,

and m 1 and m 2 are the means of the two distributions.

This form of the t statistic allows for samples that come from distribu-

tions with different standard deviations, having values of s 1 and s 2. On the

other hand, it may be the case that both distributions share a common stan-

dard deviation s. If that is the case, we can construct a t statistic by pooling

the estimates of the standard deviation from the two samples into a single

estimate, which we’ll label as s. The value of s is

s 5

Å

1 n 1212 s^2111 n 2212 s^22

n 11 n 222

The pooled two-sample t statistic would then be equal to

t 5

(^1) x 12 x 2221 m 1 2m 22
s
Å

1

n 1

1

1

n 2