An important issue for a retailer is to decide when to reorderstock from a suppl

Question

An important issue for a retailer is to decide when to reorderstock from a supplier. A common policy used to make the decision isof a type called s,S: The retailer orders at the end of a period ifthe on-hand sock is less than s, and orders enough to bring thestock up to S. The appropriate values of s and S depend ondifferent cost parameters, such as inventory holding costs and theprofit per item sold, as well as the distribution of the demandduring a period. Consequently, it is important for the retailer tocollect data relating to the parameters of the demand distribution.Suppose the following data give the numbers of a certain type ofitem sold in each of 30 weeks.

14, 8, 12, 9, 5, 22, 15, 12, 16, 7, 10, 9, 15, 15, 12, 9, 11, 16,8, 7, 15, 13, 9, 5, 19, 14, 10, 13, 7, 11

Assuming that the numbers sold each week are independent randomvariables from a common distribution, use the data to obtain a 95percent confidence interval for the mean number sold in a week.

Explanation / Answer

sample size, n =30
sample mean, x = 11.6
standard deviation, s = 4.04
standard error, e = s/n =    4.04/ 30= 0.74
degree of freedom , df = n-1 = 30-1=29
at 95% confidence, i.e =0.05, df = 29 and twotail distribution, t = 2.045                                 (fromt-table) confidence interval = x ± t*e = 11.6 ± (2.045*0.74) = (10.09,13.11) hence a 95 percent confidence interval for the mean numbersold in a week is (10.09,13.11).

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