CAIE FP2 2010 June — Question 7

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2010
SessionJune
TopicChi-squared distribution

7 Benford's Law states that, in many tables containing large numbers of numerical values, the probability distribution of the leading non-zero digit \(D\) is given by $$\mathrm { P } ( D = d ) = \log _ { 10 } \left( \frac { d + 1 } { d } \right) , \quad d = 1,2 , \ldots , 9 .$$ The following table shows a summary of a random sample of 100 non-zero leading digits taken from a table of cumulative probabilities for the Poisson distribution.
Leading digit12345\(\geqslant 6\)
Frequency222113111122
Carry out a suitable goodness of fit test at the 10\% significance level.