A firm has a large number of accounts; 40% of its accounts receivable are wholesale and...

 

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A firm has a large number of accounts; 40% of its accounts receivable are wholesale and 60% are retail. However, it is difficult to identify an account without pulling a file and looking at it. An auditor took a SRSWOR of 100 accounts and checked the balance (y in thousand dollars) of the selected accounts. Let , and s, denote the sample mean and sample standard deviation for account category h, respectively. A summary of this sample is given as follows. Nh/N n Wholesale 40% 60% 70 520 105 Retail 30 280 45 (a) Did the auditor get a stratified random sample? Why? (b) Find an unbiased estimate of the population mean ju. Suppose that the sample standard deviation is s = 170, estimate the variance of your unbiased estimator. (Ignore finite sample corrections) (c) Suppose one treats the sample as a stratified random sample with proportional allocation. Re- estimate jy using stratified sample mean and estimate the variance of this estimator. (Ignore finite sample corrections) (d) Compare the two estimation methods from (b) and (c). Explain intuitively on why one may be better than the other for this example. A firm has a large number of accounts; 40% of its accounts receivable are wholesale and 60% are retail. However, it is difficult to identify an account without pulling a file and looking at it. An auditor took a SRSWOR of 100 accounts and checked the balance (y in thousand dollars) of the selected accounts. Let , and s, denote the sample mean and sample standard deviation for account category h, respectively. A summary of this sample is given as follows. Nh/N n Wholesale 40% 60% 70 520 105 Retail 30 280 45 (a) Did the auditor get a stratified random sample? Why? (b) Find an unbiased estimate of the population mean ju. Suppose that the sample standard deviation is s = 170, estimate the variance of your unbiased estimator. (Ignore finite sample corrections) (c) Suppose one treats the sample as a stratified random sample with proportional allocation. Re- estimate jy using stratified sample mean and estimate the variance of this estimator. (Ignore finite sample corrections) (d) Compare the two estimation methods from (b) and (c). Explain intuitively on why one may be better than the other for this example.

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a In any Startified sampling method the population is subdivided ... View the full answer