704 / 762
704
Chapter 15: Chi-Square Tests
salaries of the parents is the distribution described by Benford’s
Law. That is,
= 0.301 and
= 0.179 and
= 0.125 and
= 0.301 and
= 0.079 and
= 0.067 and
= 0.058 and
= 0.051 and
= 0.046.
: At least one of the proportions of the leading digits for the salaries
of the parents specified by Benford’s Law is different. That is, there
are significant discrepancies between the distributions of the
proportions.
.:
= 507.527
.: For a level of significance
= 0.05, reject
H
0
if the computed
test statistic
= 507.527 >
= 15.507.
Conclusion
: Since 507.527 > 15.507, reject
. That is, there is
sufficient evidence to support the claim that there are significant
discrepancies between the proportions of the leading digits expected from
Benford’s Law and that observed for the reported salaries for the parents on
the FAFSA forms. Hence, the data for the salaries for the parents reported
on the forms may be subject to suspicion.
Note from
Figure 15-33
that the
P
-value = 0.0000. This
P
-value supports
the decision of rejecting the null hypothesis since its value is smaller than
the significance level of 0.05. Note, a
P-
value of 0.0000 indicates that the
difference between the distributions of the proportions is very significantly
different. That is, it is very unlikely that this difference is due to change.
SUMMARY