CHAPTER 5 



Sampling from 

 Binomial Populations 



When a population of numerical measurements involves so much 

 data that it is either impossible or unwise to attempt to analyze the 

 whole of it, sampling must be relied upon to furnish the desired 

 information. As a matter of fact, most of the statistical analyses 

 now performed involve sampling data. A multitude of examples 

 could be sited to illustrate the need for sampling, but the following 

 will suffice for the purposes of this discussion. 



(5.01) Public opinion polls. Only a small percentage of the per- 

 sons eligible for interview actually are questioned about the matter 

 under study. The sole objective of the study is to estimate the pro- 

 portions of the citizens favoring the various points of view. If the 

 question to be asked has only a yes or a no answer the results of the 

 poll will constitute a sample from a binomial population, and we 

 would be attempting to estimate p. 



(5.02) A study of the toxicities of two insecticides conducted by 

 spraying insects of a certain species with the insecticides and count- 

 ing the dead insects. This is another case of sampling a binomial 

 population; but the purposes of the investigation may be different. 

 The following question is to be answered: Is one of the sprays more 

 toxic to these insects than the other? Statistically, the question 

 becomes: Is it reasonable to suppose that the two sets of data ob- 

 tained with the two sprays are samples from the same binomial 

 population? Of course, such a study also may include the estima- 

 tion of p as mentioned in (5.01). 



(5.03) Testing the breaking strengths of concrete columns, of 

 wood or of metal beams, and of other engineering materials. Break- 

 ing strengths are measured on a continuous scale of numbers; hence 

 their populations have continuous frequency distributions. Problems 



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