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Three firms carry inventories that differ in size. Firm A's inventory contains 2000 items, firm B's inventory contains 5000 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 σ = 144. 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 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.
1. Using the finite population correction factor, compute the standard error for each of the three firms given a sample of size 50.
2. What is the probability that for each firm the sample mean will be within ±25 of the population mean μ?
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We want to estimate the population mean within 5, with a 99% confidence level. The population std dev is estimated to be 15. How large is the required sample size?
In the solution to this problem, what is n? p? q? Does it appear that both np and nq are larger than 5? Why is this an important consideration?
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They would like the margin of error of the 95% confidence interval for the proportion to be 0.05 or less. Use the guessed value p = 0.25 to find the required sample size.
The company can either settle out of court for $250,000 or go to court. If the company goes to court and loses, it must pay $825,000 plus $175,000 in court costs. If it wins in court the plaintiffs pay the court costs. Identify the states of natur..
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