Introductory Biostatistics

t¼

x 1 
x 2

SEðx 1 
x 2 Þ

where

SEðx 1 
x 2 Þ¼sp

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1

n 1

þ

1

n 2

s

s^2 p¼

ðn 1 
 1 Þs^21 þðn 2 
 1 Þs 22

n 1 þn 2 
 2

This test is referred to as atwo-sample t testand its rejection region is deter-
mined using thetdistribution atðn 1 þn 2
2 Þdegrees of freedom:

For a one-tailed test, use the column corresponding to an upper tail area

of 0.05 andH 0 is rejected if

ta
tabulated value forHA:m 1 <m 2

or

tbtabulated value forHA:m 1 >m 2

For a two-tailed test orHA:m 10 m 2 , use the column corresponding to an

upper tail area of 0.025 andH 0 is rejected if

ta
tabulated value or tbtabulated value

Example 7.5 In an attempt to assess the physical condition of joggers, a
sample ofn 1 ¼25 joggers was selected and their maximum volume of oxygen
uptake (VO 2 ) was measured with the following results:

x 1 ¼ 47 :5mL=kg s 1 ¼ 4 :8mL=kg

Results for a sample ofn 2 ¼26 nonjoggers were

x 2 ¼ 37 :5mL=kg s 2 ¼ 5 :1mL=kg

To proceed with the two-tailed, two-samplettest, we have

s^2 p¼

ð 24 Þð 4 : 8 Þ^2 þð 25 Þð 5 : 1 Þ^2

49

¼ 24 : 56

sp¼ 4 : 96

254 COMPARISON OF POPULATION MEANS