B)Be Sure to Present Each Numerical Answer with a Sentence

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Ecn. 220A

Fall 2006

Todd Easton

Midterm Exam #2

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 log on to a computer during this class period. I promise that I won’t look at other students’ monitors or exam answers. I promise that the only outside help I relied upon was my 3 x 5” card. I promise that the work I turn in is mine alone.

______

Please:

a)Answer each of the following questions on the lined paper provided, using only the front of each sheet.

b)Be sure to present each numerical answer with a sentence.

c)So I can grade the exams “blind,” please put your name only on the back of each sheet (in the upper right-hand corner).

d)Leave a substantialspace between the answers you write to each problem.

e)Show all your work.

f)When you turn in your answers, put them in number order. Behind your answers put this piece of paper, and behind that your 3x5” card. Staple the whole package together.

1) [21 pts.]An American car manufacturer advertises that a particular 2006 model car gets at least 30 miles per gallon in the city. A government agency decides to test this out. It takes a random sample of 35 cars from hundreds of thousands in the 2006 production run and calculates a sample average of 28 miles per gallon. The agency does a flawless job of sampling and of measuring the fuel efficiency of cars in its sample.

a) For starters, before you go any farther with the problem, carefully explain why it would not be fair for this agency to simply conclude the manufacturer’s claim is false, based on the sample mean being lower than the claimed mileage.

b) Now, suppose the sample standard deviation is 6 miles per gallon. Can the government agency conclude, with a 5% or smaller chance of Type I error, that the new model does not achieve the claimed mileage? Include a sketch of the relevant sampling distribution in your answer, one that includes the critical value and the test statistic.

2) [3 pts.]You are calculating a 90% confidence interval for the proportion of Democrats in Multnomah County who voted in last night’s election.

a) Should you use the z or the t score to calculate the margin of error for this interval?

b) Find the appropriate score from the table. What is it?

3) [8 pts.]How far from the truth would it be to say that a sampling distribution is a relative frequency distribution describing the distribution of values in a sample? Carefully explain your answer.

4) [12 pts.]You work for GE in light bulb production. Your boss tells you that, of a simple random sample of 100 bulbs tested from a production run of 40,000 bulbs, 3 did not meet the minimum life specified (900 hours). She wants you to calculate a 95% confidence interval for the population proportion not meeting the minimum specification. Can you give her what she wants? Explain your answer.