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 o = 100. A statistical consultant recommends that each firm take a sample of 40 items from its inventory to provide statistically valid estimates of the average cost per item. Managers of the small firm 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 40. (Round your answers to two decimal places.) firm A 16.66 firm B 15.75 firm C 15.78 (b) What is the probability that for each firm the sample mean x will be within +25 of the population mean u? (Round your answers to four decimal places.) firm A 0.8666 firm B 0.8876 firm C 0.8868
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 o = 100. A statistical consultant recommends that each firm take a sample of 40 items from its inventory to provide statistically valid estimates of the average cost per item. Managers of the small firm 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 40. (Round your answers to two decimal places.) firm A 16.66 firm B 15.75 firm C 15.78 (b) What is the probability that for each firm the sample mean x will be within +25 of the population mean u? (Round your answers to four decimal places.) firm A 0.8666 firm B 0.8876 firm C 0.8868
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter5: A Survey Of Other Common Functions
Section5.3: Modeling Data With Power Functions
Problem 6E: Urban Travel Times Population of cities and driving times are related, as shown in the accompanying...
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Transcribed Image Text: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 o = 100. A statistical consultant recommends that each firm take a sample of 40 items from its inventory to provide statistically valid
estimates of the average cost per item. Managers of the small firm 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 40. (Round your answers to two decimal places.)
firm A
16.66
firm B
15.75
firm C
15.78
(b) What is the probability that for each firm the sample mean x will be within +25 of the population mean µ? (Round your answers to four decimal places.)
firm A
0.8666
firm B
0.8876
firm C
0.8868
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