Question: Be fo d\'s law claims that numbers chosen from very large data les end

Question

Question: Be fo d's law claims that numbers chosen from very large data les end to ha e-1 as the st no zero digit disproportionately en infact research has shown that if you randomly draw a number from a very Targe data file, the probabity of gotting a number with "1 as the leading digit is about 0.301 Suppose you are an auditor for a very large corporation. The revenue report involves sample of n 276 numerical entries from the fie, and r 95 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate fie that have a first nonzero digt of 1. Test the claim that p is less than 0 301 by using a -01. What is the level of signticance? ·a millions of numbers in a large computer file. Let us say you took a random

Explanation / Answer

H0: P is not less than 0.301
H1: P is less than 0.301

Let the los be alpha = 0.1

Sample proportion p = 95/276 = 0.3442

Test Statistic
Z = (p-P) / Sqrt(PQ/n) = (0.3442 - 0.301) / sqrt(0.301*0.699/276) = 1.5646

Critical z: -1.2816
P-Value: 0.9412
Here Z value > Z critical vlaue, so we accept H0
P-value > alpha 0.05, so we accept H0
Thus we conclude that P is not less than 0.301

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