Chapter 4.1, Problem 20E

To determine

To find: The label for the two strata based on the sample.

Answer to Problem 20E

The small accounts 2631, 2592 and 1445 were selected.

Explanation of Solution

Given information:

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 $50,000; 500 are in amounts between $1000 and $50,000; and the remaining 4400 are in amounts under $1000.

Line 115-116 of table D:

61041 77684 94322 24709 73698 14526 31893 32592 14459 26056

Large accounts (amount above 50,000)

There are 100 large accounts in total.

Assign every large account a unique number between 00 and 99.

Select the first 2-digit number in line 115. The corresponding large account is selected.

Repeat until 3 unique large accounts are selected.

  $\begin{array}{l}\text{61 }\Rightarrow \text{ Select account 61}\hfill \\ \text{04 }\Rightarrow \text{ Select account 04}\hfill \\ \text{17 }\Rightarrow \text{Select account 17}\hfill \end{array}$

Thus the large accounts 61, 04 and 17 were selected.

Midsize accounts (amount between 1000 and 50,000)

There are 500 midsize accounts in total.

Assign every midsize account a. unique number between 1 and 500.

Select the first 3-digit number in line 115 (starting where we left off for the large accounts). If the number is between 001 and 500, then the corresponding midsize account is selected, else we ignore the number and select the next 3-digit number.

Repeat until 3 unique midsize accounts are selected.

  $\begin{array}{l}\text{768 }\Rightarrow \text{Ignore}\hfill \\ \text{943 }\Rightarrow \text{Ignore}\hfill \\ \text{222 }\Rightarrow \text{Select account 222}\hfill \\ \text{470 }\Rightarrow \text{Select account 470}\hfill \\ \text{973 }\Rightarrow \text{Ignore}\hfill \\ \text{698 }\Rightarrow \text{Ignore}\hfill \\ \text{145 Select account 145}\hfill \end{array}$

Thus the midsize accounts 222, 470 and 145 were selected.

Small accounts (amount below 1000)

There are 4400 small accounts in total.

Assign every small account a unique number between 1 and 4400.

Select the first 4-digit number in line 115 (starting where we left off for the midsize accounts). If the number is between 001 and 4400, then the corresponding midsize account is selected, else we ignore the number and select the next 4-digit number.

Repeat until 3 unique small accounts are selected.

  $\begin{array}{l}\text{2631 }\Rightarrow \text{Select account 2631}\hfill \\ \text{8933 }\Rightarrow \text{Ignore}\hfill \\ \text{2592 }\Rightarrow \text{Select account 2592}\hfill \\ \text{1445 }\Rightarrow \text{Select account 1445}\hfill \end{array}$

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