Chapter 4.1, Problem 12E

(a)

To determine

To explain how would you use a line of Table D to choose an SRS of three complexes from the following list.

Explanation of Solution

In the list, there are $33$ apartment complexes.

We have to assign random numbers to each complex. As each complex is equally likely to be selected, each complex should be assigned equal number of random samples.

We select two digit random numbers $01,02,03,\mathrm{.....},99(\text{removing }00\text{ as there are }33$

  $\text{apartments, we need }33\text{ or }33*2=66\text{ or }33*3=99$ or such number of random numbers to assign equal number of random numbers to each complex).

We now assign random number to flats as follows.

Flat name	Random numbers assigned
Ashley Oaks	01,34,67
Bay Pointe	02,35,68
Beau Jardin	03,36,69
Bluffs	04,37,70
Brandon Place	05,38,71
Briarwood	06,39,72
Brownstone	07,40,73
Burberry	08,41,74
Cambridge	09,42,75
Chauncey Village	10,43,76
Country Squire	11,44,77
Country View	12,45,78
Country Villa	13,46,79
Crestview	14,47,80
Del-Lynn	15,48,81
Fairington	16,49,82
Fairway Knolls	17,50,83
Fowler	18,51,84
Franklin Park	19,52,85
Georgetown	20,53,86
Greenacres	21,54,87
Lahr House	22,55,88
Mayfair Village	23,56,89
Nobb Hill	24,57,90
Pemberly Courts	25,58,91
Peppermill	26,59,92
Pheasant Run	27,60,93
Richfield	28,61,94
Sagamore Ridge	29,62,95
Salem Courthouse	30,63,96
Village Manor	31,64,97
Waterford Court	32,65,98
Williamsburg	33,66,99

Now, we need two digit random number.

In the table there are five digit random numbers.

Let us start from the second five digit random number of the lower row ( $26185$ here), take first two digits ( $26$ here) and proceed row wise to get random numbers in similar way.

Note: One may start from any place of the table, may choose digits in any pattern and may proceed in any way. This is completely up to the users choice.

(b)

To determine

To show how you use each of the digits using line $117$ to select the sample.

Explanation of Solution

In the list, there are $33$ apartment complexes.

We have to assign random numbers to each complex. As each complex is equally likely to be selected, each complex should be assigned equal number of random samples.

We select two digit random numbers $01,02,03,\mathrm{.....},99(\text{removing }00\text{ as there are }33$ $\text{apartments, we need }33\text{ or }33*2=66\text{ or }33*3=99$ or such number of random numbers to assign equal number of random numbers to each complex).

We now assign random number to flats as follows.

Flat name	Random numbers assigned
Ashley Oaks	01,34,67
Bay Pointe	02,35,68
Beau Jardin	03,36,69
Bluffs	04,37,70
Brandon Place	05,38,71
Briarwood	06,39,72
Brownstone	07,40,73
Burberry	08,41,74
Cambridge	09,42,75
Chauncey Village	10,43,76
Country Squire	11,44,77
Country View	12,45,78
Country Villa	13,46,79
Crestview	14,47,80
Del-Lynn	15,48,81
Fairington	16,49,82
Fairway Knolls	17,50,83
Fowler	18,51,84
Franklin Park	19,52,85
Georgetown	20,53,86
Greenacres	21,54,87
Lahr House	22,55,88
Mayfair Village	23,56,89
Nobb Hill	24,57,90
Pemberly Courts	25,58,91
Peppermill	26,59,92
Pheasant Run	27,60,93
Richfield	28,61,94
Sagamore Ridge	29,62,95
Salem Courthouse	30,63,96
Village Manor	31,64,97
Waterford Court	32,65,98
Williamsburg	33,66,99

Now, as we defined our procedure of choosing random numbers, we observe-

Our first random number is  $26$ . It corresponds to the complex Peppermill.

Our second random number is  $41$ . It corresponds to the complex Burberry.

Our third random number is  $75$ . It corresponds to the complex Cambridge.

So, our sample to perform in-depth interview is Peppermill, Burberry and Cambridge.

Note: If we do simple random sample (SRS) once again, the sample may be different (mostly different, same in very very rare case).