You may need to use the appropriate appendix table or technology to answer this question. Three firms carry inventories that differ in size. Firm A's inventory contains 2,000 items, firm B's inventory contains 5,000 items, and firm C's inventory contains 10,000 items. The population standard deviation for the cost of the items in each firm's inventory is a = 121. A statistical consultant recommends that each firm take a sample of 50 items from its inventory to provide statistically valid estimates of the average cost per item. Managers of the small rm state that because it has the smallest population, it should be able to make the estimate from a much smaller sample than that required by the larger firms. However, the consultant states that to obtain the same standard error and thus the same precision in the sample results, all firms should use the same sample size regardless of population size. (a) Using the finite population correction factor, compute the standard error for each of the three firms given a sample of size 50. (Round your answers to two decimal places.) firm A firm B firm C (b) What is the probability that for each firm the sample mean § will be within +25 of the population mean ? (Round your answers to four decimal places.) firm A firm B firm C

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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You may need to use the appropriate appendix table or technology to answer this question. Three firms carry inventories that differ in size. Firm A's inventory contains 2,000 items, firm B's inventory contains 5,000 items, and firm C's inventory contains 10,000 items. The population standard deviation for the cost of the items in each firm's inventory is a = 121. A statistical consultant recommends that each firm take a sample of 50 items from its inventory to provide statistically valid estimates of the average cost per item. Managers of the small rm state that because it has the smallest population, it should be able to make the estimate from a much smaller sample than that required by the larger firms. However, the consultant states that to obtain the same standard error and thus the same precision in the sample results, all firms should use the same sample size regardless of population size. (a) Using the finite population correction factor, compute the standard error for each of the three firms given a sample of size 50. (Round your answers to two decimal places.) firm A firm B firm C (b) What is the probability that for each firm the sample mean § will be within +25 of the population mean ? (Round your answers to four decimal places.) firm A firm B firm C

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