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Print yourname here: / Bus. 500, Fall 2009, Todd Easton
Final Exam
Before beginning the exam, please read the following pledge and sign it. Return this sheet with your exam answers.
I promise that I will not send or receive email, or surf the Web, during this class period. I promise that I won’t look at other students’ monitors or exam answers. I promise that the only outside material I relied upon was my two 3 x 5” cards. I promise that I have read the instructions below and that the work I turn in is mine alone.
______
Please:
a) Answer the first three questions in the space provided on the exam. Answer the last three either on the lined paper provided or in an Excel spreadsheet. Write and print your answers so they can be read sequentially, without leafing through the packet you turn in.
b) Leave a substantial space between the answers you write for Problems 4) to 6).
c) Show all your work (if you use Excel, type or copy each formula).
d) Present each numerical answer you calculate with a complete sentence (as I asked you to do for the homework).
e) Print all the sheets of your exam at the same time and let me bring them to you. Put your name in the upper, right-hand corner of each sheet. Before you print, please check Print Preview to be sure you are printing what you intend.
f) When you turn in your answers, please staple answers to Problems 4) to 6) to the back of this packet, with your 3x5” cards behind them.
1) [10 pts.] Here is a situation that might be used for a question about a hypothesis test:
"A large number of complaints have been received in the past 6 months regarding airlines losing passengers' baggage. The airlines claim the problem is nowhere near as great as newspaper articles have indicated. In fact, a Southwest Airline spokesperson claimed that 1% or less of all their passengers' bags fail to arrive at the destination with the passenger. To test this claim, a consultant identified all the airports Southwest flies from. From the bags checked with Southwest at those airports, a random sample of 800 bags was selected. Of these 800, 6 bags failed to reach the destination when the passenger arrived. Using this sample result, test Southwest Airlines' claim using a 5% significance level."
Please answer the following question about this situation:
To do a hypothesis test like this one, the relevant sampling distribution must be "normal" in shape. Would it be? Briefly explain how you know.
2) [14 pts.] Ajax, Inc. just received a very large shipment of components. Employees from the purchasing department take a random sample of 120 items from the shipment, test each item, and discover 15 are defective. Ajax’s contract with the supplier calls for defects to be 10% or less of every shipment. The supplier’s quality-control specialist, Miranda, assures Ajax the shipment meets the contract specifications.
a) Suppose Ajax’s purchasing department is only willing to take a 5% chance of mistakenly concluding Miranda is wrong. If they are going to do a formal hypothesis test, what should their null and alternative hypothesis be? [Answering with just symbols and numbers is fine.]
b) Do the hypothesis test. Based on the result, should the purchasing department conclude Miranda is mistaken? Briefly explain.
Calculations for test here:Put the conclusion and explanation here:
3) [6 pts.] The human resource manager of a telemarketing firm is concerned about the rapid turnover of the firm’s telemarketers. It appears that many do not work very long before quitting. Because of the cost of hiring and training new workers, the manager decided to examine the factors that influence workers to quit. To begin with, she reviewed the work history of a random sample of workers who have quit in the last year and recorded the number of weeks on the job before quitting and the age of each worker when originally hired. Then, she ran a regression predicting weeks of employment with age. The Excel output from this regression can be found immediately below.
Regression Statistics
Multiple R / 0.434
R Square / 0.188
Adjusted R Square / 0.178
Observations / 80
Coefficients / Standard Error / t Stat / P-value / Lower 95% / Upper 95%
Intercept / 30.633 / 1.044 / 29.338 / 0.000 / 28.554 / 32.712
Age / -0.117 / 0.027 / -4.255 / 0.000 / -0.172 / -0.062
Suppose the manager wants a measure of how well this model predicts turnover.
a) What is the best single statistic in the output for that purpose?
Put the name here:b) Quote the value the statistic takes on and explain its meaning:
4) [8 pts.] On-time delivery is one of the most important quality characteristics for many service industries, including railroads. Whereas only 67% of chemical shipments via rail are made on time, the Canadian National Railway Company--according to an article in the Wall Street Journal in 2000--makes timely delivery of chemical shipments 90% of the time. Consider a sample of 10 chemical shipments made by the Canadian National Railway Company.
a) What is the probability that 7 of the shipments arrive on time?
b) What is the probability that more than 7 of the shipments arrive on time?
5) [24 pts.] Bob works in marketing for GM. He’s just surveyed a random sample of U.S. consumers regarding their preferred brand and their income. The data in the table below present some of Bob’s results.
Salary / GM / Ford / Imports / TotalUnder $70,000 / 400 / 370 / 230 / 1000
$70,000 or over / 155 / 145 / 200 / 500
Total / 555 / 515 / 430 / 1500
a) Use PhStat’s Chi-Square Test tool and Bob’s data to decide if there is sufficient evidence to indicate that a relationship exists in the population between a consumer’s income and their brand preference. Use a 5% significance level. Briefly explain your decision.
b) Give the two requested number for US consumers preferring imports:
i) the observed frequency for consumers with salaries $70,000 or over and
ii) the expected frequency for consumers with salaries $70,000 or over.
c) Explain the link between the difference in frequencies in b) and your decision in a). Include the words “population” and “sample” in your explanation.
6) [14 points] You manage a plant near Phoenix, Arizona. You are concerned about water use, partly due to the expense and partly due to community concerns about water shortages. You take a random sample of 17 months out of the last 5 years. For those 17 months, you find the plant’s water usage, number of persons employed, number of days operating, average temperature, and amount produced. Your sample data are in:
\\storage\academic\Business\Easton\BUS 500\Water Use.xls
a) Predict water use as a function of all the other variables and present the resulting Excel output. Interpret the coefficient for production.
b) What is the residual for the first month in your sample? Briefly explain its meaning.