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.

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, $n=3+3=6$

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.

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.