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 iss = 144. A statistical consultant recommends that each firm take a sample of 50 itemsfrom 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 beable to make the estimate from a much smaller sample than that required by the largerfirms. However, the consultant states that to obtain the same standard error and thus thesame precision in the sample results, all firms should use the same sample size regardlessof population size.a. Using the finite population correction factor, compute the standard error for each ofthe three firms given a sample of size 50.b. What is the probability that for each firm the sample mean x will be within ±25 ofthe population mean m?
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
s = 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.
a. Using the finite population correction factor, compute the standard error for each of
the three firms given a sample of size 50.
b. What is the probability that for each firm the sample mean x will be within ±25 of
the population mean m?
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