118 SAMPLING FROM BINOMIAL POPULATIONS Ch. 5 



be the individual farmers' designations as member or as non-member. 

 The fraction of the total number of farmers in that county who were 

 classed as members could be the parameter p of Chapter 4. Then 

 1 — p would be the fraction who were classified as non-members on 

 the stated date. 



It is entirely possible for those same farmers to be the basis for 

 other populations. Their answers for or against a proposed new 

 federal farm policy could constitute another binomial population 

 of interest, their per-acre incomes during a specified period could 

 be another (non-binomial) population, and the sizes of their families 

 on July 1, 1953, could be still another (non-binomial) population 

 which might be of interest to some group of persons. 



The chief criterion of a good definition of a population which is 

 about to be sampled is that it make entirely clear in all important 

 respects the larger group of units to which the conclusions drawn 

 from the sample will pertain. 



Given a well-defined population, the sample obviously must be 

 taken in such a manner that the impression it produces through 

 statistical analyses will have the greatest possible chance to be 

 accurate and dependable. Naturally the facilities and economic re- 

 sources available for the sampling may be limiting factors; but it 

 will be assumed in the discussion to follow that those resources and 

 facilities are at least good enough to justify undertaking the sam- 

 pling study at all. For purposes of illustration, suppose that we wish 

 to determine public opinion in a large city regarding a political issue 

 of current interest, and that our resources allow us to interview only 

 one person per each hundred in the population. How should this 

 one per cent sample be taken? If we were to visit the few major 

 business districts we could obtain our allotted number of interviews 

 more quickly and with less cost because more persons are concen- 

 trated in these small areas during business hours; but we have no 

 assurance that the opinions of the persons we would meet there are 

 the same as those we would find in the outlying districts, for example. 

 We might consider using the telephone directory until we thought 

 of the fact that some residents do not have telephones. If we are 

 interested only in the opinions of registered voters — as is easily pos- 

 sible — we could use an official listing of those persons. It is possible 

 that for some questions which might be asked we could take a random 

 sample of names from this list and interview them as our sample. 

 Such a random sample could be taken by numbering the entries con- 

 secutively from one to the number of voters on the list and then 



