Question: Consider the monthly stock returns presented in Table 1. Using a chi-squared (χ2) goodness of fit test, test the hypothesis that the first digit of the monthly return data (ignoring any leading zeroes) follows the Benford’s Law distribution, i.e., the digit D appears as the first digit with the frequency proportional to

\[{{P}_{D}}={{\log }_{10}}\left( 1+\frac{1}{D} \right)\]

where D = 1, ... , 9. Please ensure that you clearly show the following steps.

(a) Formulate an appropriate null and alternative hypothesis.

(b) Compute the test statistic.

(c) What is the P-value of the observed statistic?

(d) Conclude whether you would or you would not reject the null hypothesis at the 10 per cent level of significance.

(e) Discuss in no more than 500 words how this test could be employed to detect data tampering. Comment on your results for part (d).