reported drinking water arsenic concentrations
in parts per billion (ppb) for 10
metropolitan
Phoenix communities and 10 communities in rural Arizona. The following summary values were
reported:
1
x
= 12.5;
2
x
= 27.5;
s
1
= 7.63; and
s
2
= 15.3.
We wish to determine whether any difference
exists in mean arsenic concentrations for metropolitan Phoenix communities and for communities in
rural Arizona. Figure 10-3 shows a normal probability plot for the two samples of arsenic concentration.
3
Montgomery & Runger, 2014, 387

Inference for Two Samples
10
2.3.
CI on the Difference in Means, Variances Unknown
Case 1:
2
2
1
2
σ
σ
=
The CI for the difference in means when both variances are equal can be developed from Eqn. 10-13.
Case 2:
2
2
1
2
σ
σ
≠
The CI for the difference in means when the assumption that
2
2
1
2
σ
σ
=
is unwarranted can be developed
from the sampling distribution of T*,
(
)
1
2
1
2
*
2
2
1
2
1
2
µ
µ
−
−
−
=
+
X
X
T
S
S
n
n
(Montgomery and Runger, 2014, 383-
392)
.