Page 107 - Modern Analytical Chemistry

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90 Modern Analytical Chemistry

4
EXAMPLE .19
Tables 4.1 and 4.8 show results for two separate experiments to determine the
mass of a circulating U.S. penny. Determine whether there is a difference in the
means of these analyses at a= 0.05.
SOLUTION
To begin with, we must determine whether the variances for the two analyses
are significantly different. This is done using an F-test as outlined in Example
4.18. Since no significant difference was found, a pooled standard deviation
with 10 degrees of freedom is calculated

1
( n A - ) s 2 A +( n B -) s 2 B
1
s pool =
n A + n B -2
0
(7 - )( .00259 ) +(5 -)( .00138 )
1
1
0
=
7 +5 -2
0
= .0459
where the subscript A indicates the data in Table 4.1, and the subscript B
indicates the data in Table 4.8. The comparison of the means for the two
analyses is based on the null hypothesis
– –
H 0 : X A = X B
and a two-tailed alternative hypothesis
– –
H A : X A ¹X B
Since the standard deviations can be pooled, the test statistic is calculated using
equation 4.20
X - X B . 3 117 -3 .081
A
t exp = = = . 134
1
n +1
( / +1
5
s pool (/ A n / B ) . 0 0459 1 7 / )
The critical value for t(0.05, 10), from Appendix 1B, is 2.23. Since t exp is less than
t(0.05, 10) the null hypothesis is retained, and there is no evidence that the two
sets of pennies are significantly different at the chosen significance level.

4
EXAMPLE .20
The %w/w Na 2 CO 3 in soda ash can be determined by an acid–base titration.
The results obtained by two analysts are shown here. Determine whether the
difference in their mean values is significant at a= 0.05.
Analyst A Analyst B
86.82 81.01
87.04 86.15
86.93 81.73
87.01 83.19
86.20 80.27
87.00 83.94