Chapter 11 Sampling Procedures 2005 ThomsonSouthWestern 1 Figure

Figure 1: 6 -Step Procedure for Drawing a Sample Step 1 Define the Target

Classification of Sampling Techniques Sampling Designs Nonprobability Samples • Convenience • Judgment • Quota

Figure 6: Distribution of Sample Means for Different Samples Sizes, Population Shapes Populations n=2

Relationship Between Parameters of Parent Population and Derived Population Parent Population Element Mean: =

Derived Population of All Possible Distinguishable Samples Element 1 2 3 4 5 6

Derived Population L xj Mean: j =1 E( x ) = x = L

Distribution of Variables in Parent and Derived Population 1 Absolute Frequency 0 Values of

Example Calculations of Generating a Confidence Interval with a Stratified Sample I II n

Size and Strata in Parent Population I. N 1 = 5000 II. N 2

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Figure 1: 6 -Step Procedure for Drawing a Sample Step 1 Define the Target Population Step 2 Identify the Sampling Frame Step 3 Select a Sampling Procedure Step 4 Determine the Sample Size Step 5 Select the Sample Elements Step 6 Collect the Data from the Designated Elements 2

Classification of Sampling Techniques Sampling Designs Nonprobability Samples • Convenience • Judgment • Quota Probability Samples • Simple Random • Statified • Proportionate • Disproportionate • Cluster • Systematic • Area 3

Figure 6: Distribution of Sample Means for Different Samples Sizes, Population Shapes Populations n=2 Sampling Distributions of mean n=5 n = 30 4

Relationship Between Parameters of Parent Population and Derived Population Parent Population Element Mean: = Variance: 2 = Total A 3 B 6 C 9 D 12 E 15 F 18 3 + 6 + 9 + 12 + 15 + 18 Xi = = N 6 10. 5 (Xi- )2 (3 -10. 5)2 +. . . +(18 -10. 5)2 = N 6 = 157. 5 = 26. 25 6 5

Derived Population of All Possible Distinguishable Samples Element 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ABC ABD ABE ABF ACD ACE ACF ADE ADF AEF BCD BCE BCF BDE BDF BEF CDE CDF CEF DEF Total 18 21 24 27 30 30 33 36 27 30 33 33 36 39 42 45 Mean Xj 6 7 8 9 10 10 11 12 9 10 11 11 12 13 14 15 6

Derived Population L xj Mean: j =1 E( x ) = x = L Variance: _2 = x 6 + 7 +. . . + 15 20 105 = 10. 5 = 20 L ( xj - E(x))2 j =1 L =(6 -10. 5)2 + (7 -10. 5)2 +. . . + (15 -10. 5)2 20 = 5. 25 7

Distribution of Variables in Parent and Derived Population 1 Absolute Frequency 0 Values of X 3 2 Absolute Frequency 1 0 Values of x 8

Example Calculations of Generating a Confidence Interval with a Stratified Sample I II n 1 = 100 x 1 = ^s 12 = Xi 1 n 2 = 100 x 2 = = 3. 2 (Xi 1 x 1 )2 =. 14 n 1 -1 ^s 22 = III ^s 32 = Xi 3 n 3 = 4. 6 (Xi 2 x 2 )2 =. 12 n 2 -1 IV n 4 = 100 n 3 = 100 x 3 = Xi 2 n 2 = 5. 8 (Xi 3 x 3 )2 =. 20 n 3 -1 x 4 = ^s 42 = Xi 4 n 4 = 7. 2 (Xi 4 x 4 )2 =. 18 n 4 -1 9

Size and Strata in Parent Population I. N 1 = 5000 II. N 2 = 25000 III. N 3 = 15000 IV. N 4 = 5000 N = 50000 L xst h=1 = Whxh Nhxh h=1 L = N = 1/10(3. 2) + 5/10(4. 6) + 3/10(5. 8) + 1/10(7. 2) = 5. 08 L sx 2 st = h=1 Whs 2 x h L = h=1 ( ) = (1/10)2 (. 14) + (5/10)2 (. 12) + (3/10)2 (. 20) 100 100 sx st 2 Nh ^h)2 (s N nh + (1/10)2 (. 18) =. 000512 100 =. 0226 10