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.

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).

Store #1 Store #2 Store #3 Store #4 Number of Accounts Receivable N1=60 N2=37 N3=81 N4=22 Sample Size n1=15 n2=9 n3=20 n4=6 Number of delinquent accounts in the sample 4 2 8 1

Explanation / Answer

Answer to part )

Proportion value for each store is as follows

p1 = 4 /15

p2 = 2/9

P3 = 8/20

p4 = 1/6

.

Answer to part b)

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

P = 15 /50 = 0.30

.

Answer to part c)

Variance = P * (1- P) / n

Where:

P = 0.30

n = 50

.

On Plugging the values we get:

V = 0.3 *0.7 /50

V = 0.0042

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