A chain department store is interested in estimating the proportion of accounts

Question

A chain department store is interested in estimating the proportion of accounts receivable that are delinquent. The chain consists of four stores. So that the cost of sampling is reduced, stratification is used with each store as a stratum. Because no information on population proportions is available before sampling, proportional allocation is used, with a total sample size of n-50. From the accompanying table estimate p the proportion of delinquent accounts for the chain, and place a bound on the error of estimation. ore #1 Store #2 Store #3 Store #4 umber of Accounts Receivable Sample Size Number of delinquent accounts in the sample 1-60 N2-37 N3-81 N4-22 1-15 9 n3-20 n4-6 a. Estimate the proportion of delinquent accounts for each store. b. Estimate the proportion of delinquent accounts using Equation (5.13) c. Estimate the variance of p-hat (stratified) using Equation (5.14).

Explanation / Answer

Solution:

a) Proportion value for each store is as follows
p1 = 4 /15
p2 = 2/9
p3 = 8/20
p4 = 1/6

b) P = (4+2+8+1)/(15+9+20+6)
= 15 /50 = 0.30

c) P = 0.30, n = 50

On Plugging the values we get:

Variance = P * (1- P) / n
= 0.3 *0.7 /50 = 0.0042

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.