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 = 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. Use z-table. Using
the finite population correction factor, compute the standard error
for each of the three firms given a sample of size 50 (to 2
decimals). Firm A Firm B Firm C What is the probability that for
each firm the sample mean will be within ± 25 of the population
mean (to 4 decimals)? Firm A Firm B Firm C