70 64 99 55 64 89 87 6562 38 67 70 60 69 78 3975 56 71 51 99 68 95 8657 53 47 50 55 81 80 98Math 3342 Final Exam August 6, 2004Answer the problems on separate paper. You do not need to rewrite the problem statements onyour answer sheets. Do your own work. Show all relevant steps which lead to your solutions. Retain this question sheet for your records. 1. The following table gives the number of days to maturity for a selection of short-terminvestments. Group these data values into a frequency distribution and construct ahistogram for the frequency distribution.2. Consider the frequency distribution given in the following table for the starting salariesof technical school graduates from a National Education Association survey. From thefrequency distribution construct the grouped mean and standard deviation of the data.Salary (thousands) Frequency Class Mark16- under 18 2 1718- under 20 0 1920 - under 22 1 2122 - under 24 3 2324 - under 26 6 2526 - under 28 9 2728 - under 30 8 2930- under 32 5 31343. An internal auditor makes 1, 2 or 3 unannounced audits each quarter with probability, respectively. What is the probability over a two-quarter period that the auditor111,,326will make more than 4 unannounced audits?22 58 40 42 43 32 3433 16 49 29 30 43 3760 41 28 35 37 51 3727 31 33 24 34 28 3942 40 31 34 38 35 294. Let A and B be events for which P(A) = 0.51, P(B) = 0.43 and P( ) = 0.64. Find:AB∪a. P( ) b. P( )AB∩AB∩c. P( ) d. P( )AB∩AB∪5. Studies show that 60% of American families use physical aggression to resolve conflict. Suppose that 20 families are to be selected at random. Find the probability that morethan half use physical aggression to resolve conflict?6. The World Almanc reports that the mean travel time to work in New York is 59 minutes. Let x be the time, in minutes, that it takes a randomly selected worker to get to work on arandomly selected day. If the travel times are normally distributed with a standarddeviation of 11 minutes, find P(55 < x < 67).7. According to the Daily Racing Form, the probability is about 0.67 that the favorite in ahorse race will finish in the money (first, second or third place). Find the probability thatin the next 200 races the favorite will finish in the money at least 150 times.8. The U.S. Bureau of Labor Statistics collects information on the ages of people in thecivilian labor force and publishes the results in Employment and Earnings. Thefollowing table summarizes the ages of 35 randomly selected people in the civilian laborforce. Construct a 90% confidence interval for the mean age, , of all people in theμcivilian labor force. Assume that the population standard deviation of age is 9.5. (Note:the sum of the data is 1,262.)9. The Health Insurance Association of America reports in Survey of Hospital Semi-PrivateRoom Charges that the mean daily charge for a semi-private room in America hospitalswas $253 in 1988. In that same year, a random sample of 30 Massachusetts hospitalsyielded a mean daily semi-private room charge of $260.68 with a standard deviation of$12.77. Does this data provide sufficient evidence to conclude that for 1988, the meandaily semi-private room charge in Massachusetts hospitals exceeded the national mean of$253? (Use a significance level of = 0.05.)α10. Surveys are conducted by the Northwestern University Placement Center, Evanston, IL,on starting salaries for college graduates. Results of the surveys can be found in thepublication The Northwestern Lindquist-Endicott Report. The following tablesummarizes for two independent random samples of 32 accounting and 35 liberal artsgraduates their starting annual salaries (in thousands). The data is given in thousands ofdollars and is rounded to the nearest hundred. At the 5% significance level, does itappear that the accounting graduates have a higher mean starting salary than liberal artsgraduates? Assume that the population standard deviation for starting salaries foraccounting graduates is $1.73 thousand and that for the liberal arts graduates is $1.82thousand.Accounting Liberal Arts24.9 20.4 23.3 20.923.4 25.3 26.8 22.624.0 22.0 21.7 23.026.2 25.9 24.8 25.325.5 20.4 22.4 24.524.9 25.4 25.8 24.222.2 22.1 21.0 24.721.5 22.5 25.4 26.620.0 16.8 21.3 20.6 21.018.7 23.8 18.3 17.7 18.019.1 21.1 19.6 19.0 18.720.8 20.4 17.1 19.519.9 19.2 19.1 17.218.3 22.7 20.0 19.220.9 19.1 20.8 20.521.4 16.3 16.3 20.5(Note: The sum of the accounting data is $759.6 thousand and the sum of the liberal artsdata is $682.9 thousand.)11. The A.C. Nielsen Company collects data on the TV viewing habits of Americans andpublishes the information in Nielsen Report on Television. The following table presentsfor 12 randomly selected married couples their weekly viewing times, in hours. At the5% significance level, does it appear that married men watch less TV, on the average,than married women?Husband Wife Husband Wife215634304135245555343138382730313015452941373517(Note: For d = husband_hours - wife_hours we have = -53 and = 815.)d∑2d∑55 51 49 50 48 54 52 5454 55 55 56 46 47 4812. In planning a new airline route, management assumed that the variance of monthpassenger traffic would be 30 (thousands of passengers). The numbers of monthlypassengers (in thousands) during the first 15 months were as follows:Assuming that the number of passengers is normally distributed, test the hypothesis thatthe variance of the monthly passenger traffic is 30 – use an = 0.05 level ofαsignificance.13. It is claimed that 40 percent of all families who own a house in California have an annualincome of $65,000 or more. A random sample of 1100 families who own houses inCalifornia reveals that 455 have an income of $65,000 or more. Construct a 98%confidence interval for the true proportion of families who own a house in California whohave an annual income of $65,000 or more.14. Consider the following table showing a relationship between Annual Income andConsumption (in thousands).ObservationiIncomexiConsumptionyi1 $50 $552 58 63.5368654 47 52.5553536565276259855569606110 50 48a. Fit a straight line to the data set by the method of least squares.b. Find a 95% confidence interval for the mean annual consumption when theannual income is $55