Question

Column Row 12345 6789012345 6789012345 6789012345 67890 28 29 30 31 32 06873 21440 75593 41373 4950217972 82578 16364 12478 37622 99659 31065 83613 69889 58869 29571 57175 55564 65411 42547 70457 03426 7293783792 91616 11075 80103 078315930913276 26710 73000 78025 73539 14621 39044 47450 03197 2787 47709 Prenumbered sales invoices are kept in a sales journal. The invoices are numbered from 0001 to 5000. a. Beginning in row 28, column 10, and proceeding horizontally in the given random number table, select a simple random sample of 10 invoice numbers b. Select a systematic sample of 10 invoice numbers. Use the random numbers in row 30, columns 29-31, as the starting point for your selection. c. Are the invoices selected in (a) the same as those selected in (b)? Why or why not? EEB Click the icon to view the table of random numbers a. Complete the list of the 10 invoice numbers that will be selected for the simple random sample below. (List the terms in the same order as they appear in the original list.) b. Complete the list of the 10 invoice numbers that will be selected for the systematic sample below. (Use ascending order.) c. Are the invoices selected in (a) the same as those selected in (b)? Why or why not? 0 A. No, the invoices selected are not the same because it would be highly unlikely that a random process would O B. No, the invoices selected are not the same because a simple random sample and a systematic sample can O C. Yes, many of the same invoices were selected because any two probability samples will yield similar select the same units as a systematic process never be the same. results

Answer 1

a. To select a random sample of size 10 from this frame. Because population size (5000) is a 4 digit number, so each assigned invoice number will have 4 digit. Because 5000 is the largest possible number, we will discard the 4 digit code sequence greater than 5000.

To select random sample we choose an arbitrary point, in this case it is given to be row 28 and column, so the first 4 digit code is 0755 i.e. invoice #755 is the first value in our sample, we will discard next 4 digit code i.e. 9341 as it is greater than 5000 , in a similar way we will select the next 9 values.

So, the 10 invoice number that selected for the simple random sample are :

755

3734

1797

2825

3641

2478

3762

2996

3106

1369

b. We first calculate the sampling interval by dividing the total number of invoices in the population (=5000) by the number we want in the sample (10). In this case, the sampling interval = 5000/10 =500

We then select a number between 1 and the sampling interval (i.e. 500) from the random number table (in this case 267). Invoice #267 is the first invoice . We then count down the list starting with invoice#267 and select each 500^th 500.

The 2^nd selected invoice is 267 + 500 = 767.

The 3^rd selected selected invoice is 267 + 2*500 = 1267

The 4^th selected selected invoice is 267 + 3*500 = 1767

The 5^th selected selected invoice is 267 + 4*500 = 2267

The 6^th selected selected invoice is 267 + 5*500 = 2767

The 7^th selected selected invoice is 267 + 6*500 = 3267

The 8^th selected selected invoice is 267 + 7*500 = 3767

The 9^th selected selected invoice is 267 + 8*500 = 4267

The 10^th selected selected invoice is 267 + 9*500 = 4767

So, the 10 invoice number that selected for the systematic sample are :

267

767

1267

1767

2267

2767

3267

3767

4267

4767

The invoices selected in (a) are not same as those in (b) because not all random samples are same.

Answer : A