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10-3 INFERENCE FOR THE DIFFERENCE IN MEANS OF TWO NORMAL DISTRIBUTIONS, VARIANCES UNKNOWN 343

99

95
90
80
70
Percentage 50
60
40
30
20
10
Figure 10-3 Normal 5 PHX
probability plot of the RuralAZ
1
arsenic concentration
data from Example 0 10 20 30 40 50 60
10-6. Arsenic concentration in parts per billion

3. H : 2
1
1
4. 0.05 (say)
5. The test statistic is

x x 0
1
2
*
t 0
2 2
s 1 s 2

n n
B 1 2
*
6. The degrees of freedom on are found from Equation 10-16 as
t 0
s 2 1 s 2 2 17.632 2 115.32 2 2
2
a b c d
n 1 n 2 10 10
v 2 2 2 2 2 2 2 2 13.2 13
1s n 2 1s n 2 317.632
104 3115.32
104
2
2
1
1
n 1 n 1 9 9
2
1
*
: if
t 2.160 or if
Therefore, using 0.05, we would reject H 0 1 2 t 0 0.025,13
*
t 0 t 0.025,13 2.160
7. Computations: Using the sample data we find
x x 2 12.5 27.5
1
*
t 0 2.77
2 2 2 2
s 1 s 2 17.632 115.32
n n B
B 1 2 10 10
*
8. Conclusions: Because t 0 2.77 t 0.025,13 2.160, we reject the null hypoth-
esis. Therefore, there is evidence to conclude that mean arsenic concentration in the
drinking water in rural Arizona is different from the mean arsenic concentration in
metropolitan Phoenix drinking water. Furthermore, the mean arsenic concentration
is higher in rural Arizona communities. The P-value for this test is approximately
P 0.016.