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Ecn. 220

Fall 2002

Todd Easton

Midterm Exam #1

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 exams. I promise that the only outside material I relied upon was my 3 x 5” card. I promise that the work I turn in is mine alone.

______

Please answer each of the following questions. Show all your work (if you use Excel, type or copy each formula). Unless a specific method of answering a question is specified, feel free to select a method of your own choosing (e.g. paper and pencil or Excel). Please write answers only on the front of each sheet you use and please put your name on the back of each sheet. I’d like to grade each exam without knowing the identity of the author. If a question is about a sampling situation, assume the population size is very large, compared to the sample, unless the question says otherwise.

1) You work for The Wall St. Journal as a reporter on the business beat. Your boss has assigned you a story on Americans’ attitudes toward business and how they are changing over time. She provided you with a spreadsheet with data from two simple random samples of Americans, one taken in 1990 and the other in 2000. Please create a joint relative frequency distribution of this data using Excel’s PivotTable feature. Include your name above the top of the table. Print out the table and write a brief explanation of your conclusions about changes in attitudes over this decade, referring to the table you printed.

You can find the data in: Fac-Stu on ‘Matisse’\Bus\Easton\Ecn. 220\Conf in Bus.xls

2) Suppose you were using the samples from problem 1) to estimate the percent of Americans who have hardly any confidence in major companies in both 1990 and 2000. One difference between those two years is the sample size: it is 899 in the year 1990 and 1896 in the year 2000. What consequence will this difference in sample sizes have for your estimates? Give a numerical answer, if you can. Whether you can give a numerical answer or not, provide an intuitive explanation of how the difference in sample size will matter. To help you answer the question: assume the population standard deviation is the same in 1990 and 2000 (and that it is.30).


3) Jim is a customer service representative at a Federal Express office, in charge of expediting late mail delivery. Suppose the probability of a package being late is 10%. Further, suppose that the typical daily volume of packages for Jim’s office is 40. Jim is predicting the number of packages he will handle on a typical day. Jim says the likelihood that he will handle exactly one late package on a particular day is approximately (.9)39 x .1 = .0016423. Is he correct? Please explain your answer.

4) A survey of subscribers to Forbes magazine showed that, during the last 12 months, 46% rented a car for business reasons, 54% rented a car for personal reasons, and 30% rented a car for both business and personal reasons.

a) What is the probability that a subscriber rented a car during the past 12 months for business or personal reasons?

b) Suppose that everyone who rented a car did so for business or personal reasons. What is the probability a subscriber did not rent a car in the last 12 months?

5) The population mean and standard deviation for SAT Verbal scores for students who took the test last year were 516 and 114. Suppose, for the moment, that the scores were normally distributed.

a) What is the likelihood that a student, drawn at random from this population, scored below a 400? Sketch a normal curve and shade in the area corresponding to this probability (the sketch does not have to be pretty!).

b) If the scores were normally distributed, what is the likelihood that a student, drawn at random from this population, scored above 700? Sketch a normal curve and shade in the area corresponding to this probability.

c) According to the College Entrance Examination Board, the 84th percentile in this distribution of SAT Verbal scores was 640. Do you think the scores are normally distributed? Please explain your answer and provide supporting evidence.