Systematic Sampling Lecture 9 Section 2 7 Robb T Koether Hampden Sydney College Wed Sep 7 2011 Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 1 25 Outline 1 Homework Review 2 1 in k Systematic Sampling 3 The Sample Size 4 Assignment 5 Answers to Even numbered Problems Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 2 25 Outline 1 Homework Review 2 1 in k Systematic Sampling 3 The Sample Size 4 Assignment 5 Answers to Even numbered Problems Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 3 25 Exercise 2 23 p 116 A class consists of 100 students Suppose that we are interested in the heights of the people in the class We could take a stratified random sample using gender as the stratification variable Suppose that it is known that 60 of the 100 students in the class are female Someone shakes a box containing the 60 female tags and with a blindfold on reaches in and draws 10 tags Then this same person shakes a box containing the 40 male tags and with a blindfold on reaches in and draws 10 tags Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 4 25 Exercise 2 23 p 116 Now we have two simple random samples one for the males and one for the females each of size 10 Suppose that the average height of the males in the sample is 70 inches while the average height for the females in the sample is 63 inches How should these two average heights be combined to produce an estimate of the average height of the people in the class Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 5 25 Solution We should use a weighted average Weight the female average with 0 60 and the male average with 0 40 The estimated average for the class is est avg 0 60 63 0 40 70 37 8 28 65 8 Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 6 25 Outline 1 Homework Review 2 1 in k Systematic Sampling 3 The Sample Size 4 Assignment 5 Answers to Even numbered Problems Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 7 25 Systematic Sampling Definition 1 in k Systematic Sampling 1 in k systematic sampling is a sampling method in which one of the first k members of the population is selected at random Then beginning with that member every k th member is selected For example if k 10 then one of the first 10 members is selected at random using randInt 1 10 Suppose member 6 is selected Then beginning with member 6 every 10th member is selected That is members 6 16 26 36 and so on Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 8 25 Systematic Sampling 1 in k Systematic Sampling Number the members of the population 1 through N Using randInt 1 k choose a random starting point in the first block of size k That represents the first member of the sample From that starting point put every k th member in the sample Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 9 25 Example Example 1 in 5 Systematic Sampling There are 19 students in this class Let s choose a 1 in 3 systematic sample from the 19 students in the class Use randInt 1 3 to choose the first member It will be a random number from 1 to 3 Then choose every 3rd student thereafter Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 10 25 Outline 1 Homework Review 2 1 in k Systematic Sampling 3 The Sample Size 4 Assignment 5 Answers to Even numbered Problems Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 11 25 The Sample Size In the last example notice that 19 3 6 13 So the sample size could end up being either 6 or 7 depending on the starting point If the starting point is 1 then we get 7 members 1 4 7 10 13 16 19 If the starting point is 2 then we get 6 members 3 5 8 11 14 17 Either way each member has a 1 3 chance of being in the sample right Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 12 25 The Sample Size Carry out the selection using a seed of 15 Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 13 25 The Sample Size The population Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 14 25 The Sample Size The blocks Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 14 25 The Sample Size Y The randomly selected member from the first block Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 14 25 The Sample Size Y N N Y Y N N The sample Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 14 25 The Sample Size Now carry out the selection again using a seed of 14 Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 15 25 The Sample Size The population Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 16 25 The Sample Size The blocks Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 16 25 The Sample Size N The randomly selected member from the first block Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 16 25 The Sample Size N Y N Y Y N The sample Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 16 25 How to Determine k The Determination of k Divide the population size N by the desired sample size n Let k N n rounded off If you round down you may get one extra member If you round up you may get one less member It does not matter Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 17 25 Example Example Systematic Sampling Suppose we want to select n 12 members from a population of size N 187 7 Compute k 187 12 15 12 16 Use randInt 1 16 to get a random integer from 1 to 16 Then include that number and every 16th number thereafter in the sample Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 18 25 Outline 1 Homework Review 2 1 in k Systematic Sampling 3 The Sample Size 4 Assignment 5 Answers to Even numbered Problems Robb T Koether Hampden Sydney College Systematic Sampling Wed Sep 7 2011 19 25 Assignment Homework Read Section 2 7 pages 117 121 Let s Do It 2 9 2 10 Page 121 exercises 28 30 32 Chapter 2 review p 136 exercises 44 46 48 50 51 53 55 56 63 Robb T Koether Hampden …
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