Question

Sampling by accountants Accountants often use stratified samples during audits to verify a company’s records of such things as accounts receivable. The

stratification is based on the dollar amount of the item and often includes $100\%$ sampling of the largest items. One company reports $5000$ accounts receivable. Of these, $100$ are in amounts over $\backslash (50,000;500$ are in amounts between $\backslash )1000and\backslash (50,000;$ and the remaining $4400$are in amounts under $\backslash )1000$Using these groups as strata, you decide to verify all the largest accounts and to sample $5\%$ of the midsize accounts and $1\%$of the small accounts. How would you label the two strata from which you will sample? Use Table D, starting at line $115$ to select only the first$3$ accounts from each of these strata.

Short answer

The small accounts $2631,2552$ and $1445$ were selected.

Step-by-step solution

Given information

Total No. of accounts receivable =$500$

No. of accounts receivable amounts over $\$50,000=100$

No. of accounts receivable amounts between $\$1000and\$50,000=500$

No. of accounts receivable amounts under $\$1000=4400$

A sample size of $5\%$ of the midsize accounts = $500\times 0.05=25$

A sample size of $1\%$ of small accounts = $440\times 0.01=44$

A sample size of $100\%$ sampling of the largest items = $100\times 1=100$

Total sample size, $n=3+3=6$

Concept

A simple random sample (SRS) of size $n$ is made up of n people chosen from the population with an equal chance of being the sample that is actually chosen.

Calculation

The stratification is based on the item's financial value, and it frequently contains a $100$percent sample of the most expensive things. $5000$accounts receivable are reported by one company. There are $100$in sums greater than $\$50,000500$in amounts between $\$1000$and $\$50,000$and $4400$in amounts less than $\$1000$

Line $115-116$of table D:$61041776849432224709736981452631893325921445926056$

Significant accounts (amount above $50,000$)

There are a total of $100$major accounts.

Assign a unique number between $00$and $99$to each major account.

In line $115$choose the first two-digit number. The appropriate huge account is chosen.

Repeat until three distinct large accounts have been chosen.$$\begin{gathered} 61\Rightarrow Selectaccount61 \\ 04\Rightarrow Selectaccount04 \\ 17\Rightarrow Selectaccount17 \end{gathered}$$

As a result, the huge accounts $61,04$and $17$were chosen.

Medium-sized businesses (amount between $1000$ and $50,000$)

In total, there are $500$ midsize accounts.

Assign a unique number between $1$ and $500$ to each midsize account.

In line $115$ choose the first three-digit number (starting where we left off for the large accounts). If the number is between $001$ and $500$ the associated midsize account is chosen; otherwise, the number is ignored and the next $3-$digit number is chosen.

As a result, the big accounts $61,04$ and $17$were chosen.

Accounts in the middle (amount between $1000$ and $50,000$)

In total, there are $500$ medium accounts.

Assign a distinct number between $1$ and $500$ to each medium-sized account.

In line $115$choose the first three digits (starting where we left off for the large accounts). If the number falls between $001$and $500$the associated midsize account is chosen; otherwise, the number is ignored and the next three-digit number is chosen.

Repeat until $3$ unique midsize accounts are selected.$$\begin{gathered} 768\Rightarrow Ignore \\ 943\Rightarrow Ignore \\ 222\Rightarrow Selectaccount222 \\ 470\Rightarrow Selectaccount470973\Rightarrow Ignore \\ 698\Rightarrow Ignore \end{gathered}$$

$145$Select account $145$

As a result, the $222,470$and $145$midsize accounts were chosen.

Small business accounts (amount below $1000$)

In total, there are $4400$ tiny accounts.

Assign a unique number between $1$ and $4400$ to each tiny account.

In line $115$ choose the first four-digit number (starting where we left off for the midsize accounts). If the number is between $001$ and $4400$ the associated midsize account is chosen; otherwise, the number is ignored and the next $4$-digit number is chosen.

Repeat until $3$ unique small accounts are selected.$$\begin{gathered} 2631\Rightarrow Selectaccount2631 \\ 8933\Rightarrow Ignore \\ 2592\Rightarrow Selectaccount2592 \\ 1445\Rightarrow Selectaccount1445 \end{gathered}$$

Thus the small accounts $2631,2592$and $1445$ were selected.