Introductory Biostatistics

za
tabulated value or zbtabulated value

This test is referred to as theone-sample t test.

Example 7.1 Boys of a certain age have a mean weight of 85 lb. An observa-
tion was made that in a city neighborhood, children were underfed. As evi-
dence, all 25 boys in the neighborhood of that age were weighed and found to
have a meanxof 80.94 lb and a standard deviationsof 11.60 lb. An applica-
tion of the procedure above yields

SEðxÞ¼

s

ffiffiffi

n

p

¼

11 : 60

ffiffiffiffiffi

25

p

¼ 2 : 32

leading to

t¼

80 : 94
85

2 : 32

¼
1 : 75

The underfeeding complaint corresponds to the one-sided alternative

HA:m< 85

so that we would reject the null hypothesis if

ta
tabulated value

From Appendix C and with 24 degrees of freedomðn
1 Þ, we find that

tabulated value¼ 1 : 71

under the column corresponding to a 0.05 upper tail area; the null hypothesis is
rejected at the 0.05 level. In other words, there is enough evidence to support
the underfeeding complaint.

7.2 ANALYSIS OF PAIR-MATCHED DATA

The method presented in this section applies to cases where each subject or
member of a group is observed twice (e.g., before and after certain interven-
tions), or matched pairs are measured for the same continuous characteristic.

248 COMPARISON OF POPULATION MEANS