name, day & time of your class [Return to 3310] BUS 220 Since this is a take home exam, it will be strictly graded & remember if I can't read or follow your solution, I can't grade it. All answers should be neat, orderly, well labeled & professional in appearance. If you use a computer to calculate any part of your answer, make it easy for me to understand what you did. Support all conclusions with appropriate statistical analysis. Turn the exam in to me, on paper, not electronically, or one of my administrative assistants in Room 3310 [ask them to put it in my mailbox] or via fax at 610.325.2813. rev 5/16 Deadline for this exam is listed in the course syllabus. 1. Extraprice Rental Car rented 6 different vehicle types last year at the frequencies shown in the table: a. Prepare a frequency columnar chart [use Excel for parts a, b & c] b. Prepare a relative frequency columnar chart Vehicle Type c. Prepare a pie chart showing relative frequency Sub-compact d. If a 20 % increase in all rentals is expected for next year, how many luxury rentals Compact should they expect? Full-size Luxury SUV Van Total Frequency 545 892 740 360 280 168 2985 2. Kerbeck Automotive Sales pays its sales staff a salary plus a commission on sales. The mean biweekly commission is $990, the median $950, and the standard deviation $70. The shape of the distribution is unknown. Estimate the percent of salespeople that earn more than $885, but less than $1095 in commissions. 3. Listed below are the selling prices (in thousands of dollars) for a sample of 19 lakeside lots at Deep Creek Lake, a vacation home community in the Allegheny mountains of western Maryland. 86 39 28 25 82 61 142 85 50 120 148 140 90 85 137 81 65 92 85 Determine the following: a. the first quartile b. the third quartile c. the median d. Draw a box plot for the data. 4. Find the probability that 1 of the first 4 batters in the Allentown Iron Pigs batting order gets a hit, if the probability of getting a hit is .240. 5. The length of time a domestic flight must wait between gate departure and takeoff taxi at BWI International Airport is approximately normally distributed with a mean of 22 minutes and a standard deviation of 7 minutes. a. What is the probability that a plane must wait between 18 and 24 minutes before taxiing for takeoff after leaving the gate? b. What is the probability a plane must wait between 22 and 30 minutes before taxiing for takeoff after leaving the gate? c. What is the probability a plane waits more than 12 minutes between gate departure and takeoff taxi? d. What is the length of time such that only 5% of planes wait this long or longer before gate departure and taxiing to the runway? . 6. The American College of Cardiologists claims that the mean number of grams of fat in the popular M.I. Burger sold at Burgers To Die For is 24 grams with = 5 grams. If a sample of 50 M. I. Burgers is taken, what is the probability that the sample mean is 25 grams or more? 7. Useless Airways advertises that, on average, its New York to London flight takes five hours and 30 minutes. The Federal Trade Commission randomly selects ten New York to London flights on Useless and finds that the sample mean is 5 hours with a sample standard deviation of 0.8 hour. a. What is the point estimate of the population mean? b. Construct a 95 percent confidence interval for the population mean. c. Explain what distribution is used for this problem & why. d. Is it reasonable for Useless to claim a mean flight time of 5 hours and 30 minutes? Why? 8. Phillies' second baseman, Cesar Hernandez, has a batting average of .289. Assume that's the probability of him getting a hit in any single at bat. If he has three at bats, find the probability that : a. He gets three hits. b. He gets no hits. c. He gets at least one hit. 9. A typical college student spends an average of 2.4 hours a day using a computer. A sample of 13 students at IUP revealed the following number of hours per day using the computer. Can we conclude at a 98% level of confidence, that the mean number of hours per day using the computer by students at IUP is the same as the typical student's usage? 3.15 3.25 2.20 2.40 2.65 2.95 2.75 2.85 2.95 2.45 1.95 2.35 3.85 10. A recent MBA graduate, who is not too bright, is trying to decide between two job offers, one in Trenton and one in Maui. DUH! One factor affecting his decision is the cost of a new home in each city. A recent study sampled 66 new home sales in the Trenton area and found that the mean selling price of a new home was $176,900 with a population standard deviation of $59,000. A similar Maui study based on a sample of 54 new home sales found that the mean selling price was $198,500 with a population standard deviation of $49,800. Conduct a test at the .034 level of significance to determine if there is any real difference in the mean selling price of new homes in these two cities. 11. Whonose Economic Forecasting, Inc. and Wazzup Econometrics have the same mean error per year in forecasting the stock market over the last ten years. However, the standard deviation for Whonose is 40 points and 30 points for Wazzup. At the 0.05 significance level can we conclude that Wazzups and Whonose have different variations? 12. The federal minimum hourly wage has not changed since 1997. The federal minimum hourly wage rates for selected years between 1975 and 1997 are shown. Using 1975 as the base period, develop an index that shows the changes in hourly wages. Year 1975 1980 1985 1990 1995 1996 1997 Hourly Wage $2.10 3.12 3.35 3.90 4.25 4.85 5.35 13. In recent years, 22 percent of the American made automobiles sold in the United States were manufactured by General Motors, 24 percent by Ford, 6 percent by Daimler-Chrysler, and 48 percent by all others. A sample of the sales of American-made automobiles conducted last week revealed that 36 were manufactured by Daimler Chrysler, 220 by Ford, 125 by GM, and 345 by all others. Do these observations fit with the expected values at a .01 level of significance? 14. If you buy 12 lb of Possum meat for $2/lb, then 20 lb for $1.50/lb & 7 lb for $4/lb, the average price you paid was $2.43/lb, right? 15. Ripoff Coffee Co. sells coffee in cans that they promise contain a minimum of 2 pounds. U. R. Busted, an inspector for the FTC [Federal Trade Commission], takes a sample of 42 cans to see if they actually contain at least 2 lbs at a .0102 level of significance. His sample results: x-bar = 1.92 lb with = .22 lb. What will U.R. find? 16. The flight times for the trip from Altoona to Pittsburgh varies between 1 hour & 25 minutes & 55 minutes, depending on the local mountain weather patterns. No flight times are anymore likely than any other. The trip is scheduled to take 1 hour & 10 minutes, find the probability of: a. Arriving at most 10 minutes late. b. A flight time between 1 hour & 1 hour & 15 minutes. c. Arriving at least 5 minutes early. 17. To enter the University of Pennsylvania's Veterinary School you must score in the 98.9 percentile in the VCAT exam. If the mean score is 204 with a standard deviation of 8, will your 221 get you in? 18. Using Excel, conduct a regression analysis for the following data comparing vehicle weight with fuel efficiency, including: a. Trendline chart b. Equation c. Correlation Coefficient d. Written characterization of results. 19. From the data in problem 18: a. Is the Toyota Prius mpg an outlier? b. If not, what MPG would make it an outlier? Vehicle Buick LeSabre Ford Expedition Toyota Corolla Saturn Coupe Ford F-150 Pontiac Bonneville Honda Civic Cadilliac Escalade Hummer H1 Ford Mustang Lincoln Navigator Dodge Neon Scion xB Chevrolet Camero PT Cruiser Toyota Prius Weight 3565 4855 2640 2370 3805 3590 2935 5115 6600 3065 3425 2560 2850 3205 3200 3950 MPG 19 15 35 28 15 19 30 12 10 20 16 28 36 19 20 55 20. Using only the Empirical Rule [use .68, .95, .99], find the following: a. The area between -3 and +2 standard deviations. b. The area between 2 & 1 standard deviations above the mean. c. What percentile lives at 2 standard deviations above the mean? d. The area between the mean & 3 standard deviations below the mean