STAT211 HW5: Detecting fraud? You may work with in a group of as many as three students on this assignment, handing in one report with all names, provided that you all contribute to the work. You must submit a word- processed report, with computer output integrated into your report as appropriate. The leading digit of a numerical quantity is the first non-zero digit when reading from left-to- right. For example, the closing price of Apple Inc. stock on January 26, 2018 was $171.51, which has a leading digit of 1. The closing price for American Airlines stock on that date was $53.07, which has a leading digit of 5. The leading price of Adobe Systems stock was $201.30, which has a leading digit of 2. A hypothesis attributed to a statistician/ physicist named Benford is that 30% of all numerical quantities have a leading digit of 1. The Benford hypothesis can be written as He: It =.30. (The Benford hypothesis can be used to detect fraud. If people make up fictitious numerical quantities, for example on a tax return, they are unlikely to think about whether their made-up numbers follow Bexford's hypothesis. So, as a first step to detect potential fraud, investigators could perform a test of whether the leading digits of the numerical quantities on the tax return reveal a significant difference from Boogerd's hypothesis.) To investigate the Benford hypothesis, I collected data (from www.nasdaq.com/quotesasdaq- 100-stocks.aspx) on closing prices of 104 stocks, as of January 26, 2018. I found that 29 of the 104 stocks had a closing price with a leading digit of 1. Consider this to be a representative sample from the population of all stock prices. a) Check whether the sample size condition for a one-proportion z-test is satisfied. b) Determine the value of the z-test statistic. (Show how to calculate this by hand.) c) Interpret the value of this test statistic. d) Determine the p-value of the test. c) Describe what this p-value means (probability of what, assuming what?). f) Would you reject the null (Benford) hypothesis at the .05 significance level? g) Determine a 95% one-proportion z-interval based on this sample. (Show how to calculate this by hand.) h ) Interpret what this interval means/reveals.i) Is the Benford value within the confidence interval? Is this consistent with your test decision? Explain. j) Suppose that you want to repeat this study with a new sample of data. Determine the sample size needed to achieve a margin-of-error of .03 with a confidence level of95% =