University of Wisconsin-Milwaukee Lubar School of Business BUSADM 210 Layth C. Alwan Homework #6 - Due Wednesday July 12, 2017 1) 2) Exercise 7.20, p. 375 Suppose that a psychologist thinks that age, up to a certain age, influences IQ positively. Below is a random sample of persons whose IQs had been tested at age 16 and then at middle-age (thus, the same persons are involved at sixteen and at middle age): Person 1 2 3 4 5 6 7 8 9 10 Sixteen 90 103 89 92 103 96 110 92 103 102 Middle Age 101 108 91 87 103 96 112 95 107 109 Test H 0 : sixteen middle_ age vs. H 1 : sixteen middle _ age at the 5% level of significance. 3) The \"fog index\" is used to measure the reading difficulty of a written text. Suppose random samples of 10 pages of material from Wall Street Journal and Sports Illustrated had the following sample results: Test if the population mean fog index for the Wall Street Journal is greater than the population mean fog index for Sports Illustrated, that is, H 0 : Wall Sports vs. H 1 : Wall Sports at the 5% level of significance. Do not assume equal variances of the underlying populations. 4) Exercise 7.40, p. 382 5) Exercise 8.28, p. 433 6) Exercise 8.70, p. 450 7) A national survey of restaurant employees found that 75% said that work stress had a negative impact on their personal lives. A sample of 100 employees of a restaurant chain finds that 68 answer 'Yes\" when asked, \"Does work stress have a negative impact on your personal life?\" Is this good reason to think that the proportion of all employees of this chain who would say \"Yes\" differs from the national proportion? Test at 5% level. 8) Statistics can be used to detect fraud. There is a pattern that turns up when observing the leading digit in real data (as opposed to fake data like you might find in falsified financial records). That pattern is expressed by Benford's law. The table below lists the percentages for leading digits from Benford's Law that we would expected to observe. It also list the number of leading digits actually observed on a batch of 784 checks that are believed to be fraudulent. Leading 1 2 3 4 5 Digit Bedford's 30.1% 17.6% 12.5% 9.7% 7.9% Law Observed 0 15 0 76 479 Leading Digit of 784 Checks Investigated for Fraud 6 7 8 9 6.7% 5.8% 5.1% 4.5% 183 0 8 23 Use this data to test the claim at the 1% significance level that there is a significant discrepancy between the leading digits expected from Benford's Law and the leading digits from the 784 checks. 9) A traffic-safety researcher has observed vehicles at a stop sign in a suburban neighborhood and recorded (1) the type of vehicle (sedan, SUV, pickup truck) and (2) driver behavior at the stop sign (complete stop, near stop, \"ran\" the stop sign). At the 5% level of significance, test if there is a relationship between driver behavior and type of vehicle. Sedan SUV Pickup Stopped 183 54 14 Coasted 107 27 20 Ran It 60 19 16