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2006-Spring-Final

# 2006-Spring-Final - ISMT111 Business Statistics(L1 Final...

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ISMT111 Business Statistics (L1) Final exam May 27, 2006 Directions 1. There are 6 pages in this examination paper (including this). Check to make sure you have a complete set and notify the invigilator immediately if part of it is missing. 2. Key formulas and statistical tables ( z and t ) are provided separately. 3. Calculator may be used in this examination. 4. You are given 3 hours to complete this examination. Do not begin until you are told to do so. 1

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1. (22pts) American International Paper Corporation must purchase a new papermaking machine. The company must choose between two machines, machine 1 and machine 2. Since the machines produce paper of equal quality, the company will choose the machine that produces the most paper in a one-hour period (measured in rolls of paper per hour). Two designs are adopted to compare the two machines. ( Design A ): Five randomly selected machine operators produce paper for one hour using machine 1, and another °ve randomly selected machine operators produce paper for one hour using machine 2 (there are a total of 10 machine operators). The following results are obtained. Hourly production of paper Machine 1 45 47 45 44 44 Machine 2 42 44 43 41 43 (a) At the 0.05 level of signi°cance, can you conclude that the average hourly production from two machines are di/erent? (b) What is the p-value for the testing in (a) (c) What assumption(s) did you make in doing (a) (d) Construct a 95% con°dence interval for ° 1 ° ° 2 ( Design B ): Suppose, instead of using 10 machine operators, the company decides to randomly select °ve machine operators. Each produces paper for one hour using machine 1, then produces paper for one hour using machine 2. The data is shown below: Hourly production of paper Operator: 1 2 3 4 5 Machine 1 45 47 45 44 44 Machine 2 42 44 43 41 43 e. At the 0.05 level of signi°cance, can you conclude that the average hourly production from two machines are di/erent? f. What is the p-value for the testing in (e) g. What assumption(s) did you make in doing (e) h. Construct a 95% con°dence interval for ° 1 ° ° 2 2
2. (14pts) The State Environmental Protection Agency (SEPA) is responsible for monitoring the air pollution level for a large western metropolis. The air pollution level is considered to be acceptable (or

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