Question

3.66  Random digit telephone dialing. An opinion poll in California uses random digit dialing to choose telephone numbers at random. Numbers are selected separately within each California area code. The size of the sample in each area code is proportional to the population living there.

1. (a) What is the name for this kind of sampling design?

2. (b) California area codes, in rough order from north to south, are

209	213	310	323	341	369	408	415	424	442
510	530	559	562	619	626	627	628	650	657
661	669	707	714	747	752	760	764	805	818
831	858	909	916	925	935	949	951

Another California survey does not call numbers in all area codes but starts with an SRS of eight area codes. Choose such an SRS. If you use Table B, start at line 132.

TABLE B Random Digits

Line
101	19223	95034	05756	28713	96409	12531	42544	82853
102	73676	47150	99400	01927	27754	42648	82425	36290
103	45467	71709	77558	00095	32863	29485	82226	90056
104	52711	38889	93074	60227	40011	85848	48767	52573
105	95592	94007	69971	91481	60779	53791	17297	59335
106	68417	35013	15529	72765	85089	57067	50211	47487
107	82739	57890	20807	47511	81676	55300	94383	14893
108	60940	72024	17868	24943	61790	90656	87964	18883
109	36009	19365	15412	39638	85453	46816	83485	41979
110	38448	48789	18338	24697	39364	42006	76688	08708
111	81486	69487	60513	09297	00412	71238	27649	39950
112	59636	88804	04634	71197	19352	73089	84898	45785
113	62568	70206	40325	03699	71080	22553	11486	11776
114	45149	32992	75730	66280	03819	56202	02938	70915
115	61041	77684	94322	24709	73698	14526	31893	32592
116	14459	26056	31424	80371	65103	62253	50490	61181
117	38167	98532	62183	70632	23417	26185	41448	75532
118	73190	32533	04470	29669	84407	90785	65956	86382
119	95857	07118	87664	92099	58806	66979	98624	84826
120	35476	55972	39421	65850	04266	35435	43742	11937
121	71487	09984	29077	14863	61683	47052	62224	51025
122	13873	81598	95052	90908	73592	75186	87136	95761
123	54580	81507	27102	56027	55892	33063	41842	81868
124	71035	09001	43367	49497	72719	96758	27611	91596
125	96746	12149	37823	71868	18442	35119	62103	39244
126	96927	19931	36089	74192	77567	88741	48409	41903
127	43909	99477	25330	64359	40085	16925	85117	36071
128	15689	14227	06565	14374	13352	49367	81982	87209
129	36759	58984	68288	22913	18638	54303	00795	08727
130	69051	64817	87174	09517	84534	06489	87201	97245
131	05007	16632	81194	14873	04197	85576	45195	96565
132	68732	55259	84292	08796	43165	93739	31685	97150
133	45740	41807	65561	33302	07051	93623	18132	09547
134	27816	78416	18329	21337	35213	37741	04312	68508
135	66925	55658	39100	78458	11206	19876	87151	31260
136	08421	44753	77377	28744	75592	08563	79140	92454
137	53645	66812	61421	47836	12609	15373	98481	14592
138	66831	68908	40772	21558	47781	33586	79177	06928
139	55588	99404	70708	41098	43563	56934	48394	51719
140	12975	13258	13048	45144	72321	81940	00360	02428
141	96767	35964	23822	96012	94591	65194	50842	53372
142	72829	50232	97892	63408	77919	44575	24870	04178
143	88565	42628	17797	49376	61762	16953	88604	12724
144	62964	88145	83083	69453	46109	59505	69680	00900
145	19687	12633	57857	95806	09931	02150	43163	58636
146	37609	59057	66967	83401	60705	02384	90597	93600
147	54973	86278	88737	74351	47500	84552	19909	67181
148	00694	05977	19664	65441	20903	62371	22725	53340
149	71546	05233	53946	68743	72460	27601	45403	88692
150	07511	88915	41267	16853	84569	79367	32337	03316

Answer 1

Solution

Part (a)

Name of the sampling design: PPS (Probability Proportional to Size) Sampling. Answer 1

Explanation:

In SRS (Simple Random Sampling), all population units have equal chance (probability) of being selected into the sample. Under PPS, the population consists of a number of sub-populations with varying number of units and the chance (probability) of being selected into the sample depends on the size of the sub-population.

Part (b)

Procedure:

Step 1

Serially number the given area codes from left to right Line 1 down to Line 4, as shown below:

1	2	3	4	5	6	7	8	9	10
209	213	310	323	341	369	408	415	424	442
11	12	13	14	15	16	17	18	19	20
510	530	559	562	619	626	627	628	650	657
21	22	23	24	25	26	27	28	29	30
661	669	707	714	747	752	760	764	805	818
31	32	33	34	35	36	37	38
831	858	909	916	925	935	949	951

Step 2

With the given excerpt of random numbers, starting from Line 132 and moving towards right, pick up 2-digit numbers. Discard a random number if it is greater than 76 [38 x 2].

Divide the picked random number by 38 and obtain the remainder. If this remainder is a repeat, again discard the random number.

Continue the process till 8 acceptable numbers are obtained.

Step 3

Select the area code corresponding to the accepted result in the above step as sample.

Actual sampling   

Random Number	68	73	25	52	59	84	29	20	87	96	43
Sr.No. of area code	30	35	25	14	21	R	29	20	R	R	5
Area code	818	925	747	562	661	-	805	657	-	-	341

Thus, the sample consists of area codes:

341, 562, 657, 661, 747, 805, 818 and 925. Answer 2

DONE