206
I N D U S T R I A L AND E N G I N E E R I N G CHEMISTRY Table VI.
Material
Determination of Lead
Lower Limit 2.39 11.7 9.6 24.1
MgCOs
ZnO Zn stearate Ocher CaCO:
Upper Limit 3.16 20.3 17.0 49.9 0.32 60.9 3.33 22.9 25.6
-47.1 0.16 - 12.5 0.63
Ti02
.Talc Kaolin Bas04
23.2
Central Value 2.78 16.0 13.3 37.0 0.08 64.0 1.45 17.7 24.4
efficient-Le., a probability indicating in what fraction of cases the confidence interval will, in the long run, actually cover the true value; and ( b ) to judge, in any given case, whether the result is significantly different from 0. The t test is here appropriate and will rovide a n answer to both questions. Thus for magnesium carionate (first item in Table V) we find: Mean of sample determinations = f = 7 . 9 difference: d = Mean of blank determinations = jj = 2 . 3 5 ) f - ?j = 5.55
We conclude that d is significantly different from 0. Confidence limits for d ate found as follows: Table value for t corresponding to P = 0.05: t = 4.30
(0.18) X (4.30) = 0.77 0.77 = 4.78 { 5 5555 +- 0.77 = 6.32 Finally, for 1 gram of magnesium carbonate, the limits are:
2.39 and 3.16 p.p.m. of Pb Results obtained in a similar fashion for the eight other items together with the corresponding central values, are given in Table VI. I t is seen that in the case of calcium carbonate and talc the lower limit is negative; the interval includes 0, which, as we know, is to be interpreted as indicating that the observed difference in p.p.m. of lead between sample and blank is not significantly different from 0. I n other words, there is no evidence, on the 5% level of significance, for considering the sample as containing more lead than the blank.
‘
Estimate of variance for a single determination:
l(7.8 st =
-
-
1)
Degrees of freedom = (2
+ (2 - 1)
1)
+ (2 - 1) = 2
Estimate of variance of d: 8:
LITERATURE CITED
- 7.9)s + (8.0 - 7.9)*)+ { (2.2 - 2.35)’ + (2.5 - 2.35)*) = o.0325 (2
= Sf
+ t =
SI
2
= 0.0325 -
2
+
0.0325 = o.0325 2
5.55 = 5.55 d0.0325 = 0.18
30’8
Corresponding prohahility (found in t table for 2 degrees of freedom) :
P
=
0.001 (approximately)
Vol. 17, No. 4
(1) Coulliette, J. H.,IND.ENG.C H ~ MANAL. ., ED., 15, 732-4 (1943). (2) Fisher, R. A., “Statistical Methods for Re-
search Workers”, New York, G. E. Stechert & Co., 1941.
