Again, suppose you are the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank (see Problem 7). You draw a random sample of n = 228 numbers from this file and r = 92 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1.
i. Test the claim that p is more than 0.301. Use α = 0.01.
ii. If p is in fact larger than 0.301, it would seem there are too many numbers in the file with leading 1’s. Could this indicate that the books have been “cooked” by artificially lowering numbers in the file? Comment from the point of view of the Internal Revenue Service. Comment from the perspective of the Federal Bureau of Investigation as it looks for “profit skimming” by unscrupulous employees.
iii. Comment on the following statement: “If we reject the null hypothesis at level of significance α, we have not proved H0 to be false. We can say that the probability is α that we made a mistake in rejecting H0.” Based on the outcome of the test, would you recommend further investigation before accusing the company of fraud?
Please provide the following information:
(a) What is the level of significance? State the null and alternate hypotheses.
(b) What sampling distribution will you use? Do you think the sample size is sufficiently large? Explain. Compute the value of the sample test statistic.
(c) Find the P-value of the test statistic. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a)–(c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(e) Interpret your conclusion in the context of the application.