Applied Statistics and Probability for Engineers

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

3. H 1 :  1   2


4.  0.05 (say)


5. The test statistic is


6. The degrees of freedom on are found from Equation 10-16 as

Therefore, using 0.05, we would reject H 0 :  1  2 if t0.025,132.160 or if

t0.025,132.160

7. Computations: Using the sample data we find


8. Conclusions: Because  2.77t0.025,13 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.

t* 0

t* 0 

x 1 x 2

B

s^21

n 1

s^22

n 2



12.527.5

B

1 7.63 22

10

1 15.3 22

10

2.77

t* 0

t* 0

v

a

s 12

n 1

s 22

n 2 b

2

1 s 12

 n 122

n 1  1

1 s 22

 n 222

n 2  1



c

1 7.63 22

10

1 15.3 22

10

d

2

31 7.63 22

1042

9

31 15.3 22

1042

9

13.2 13

t* 0

t* 0 

x 1 x 2  0

B

s 12

n 1

s 22

n 2

1

0

5

10

20

30

40

50

60

70

80

90

95

99

Percentage

10 20 30 40 50

PHX

RuralAZ

60

Arsenic concentration in parts per billion

Figure 10-3 Normal

probability plot of the

arsenic concentration

data from Example

10-6.

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