Some General Results of Elementary Sampling Theory 

 for Engineering Use 



By PAUL p. COGGINS 



E\'ERY day we base conclusions on the results of the process 

 commonly known as "sampling." For example, if five times 

 in a week a man has waited ten minutes or more for his trolley at a 

 street corner, he may conclude that the transportation facilities are 

 poor. Or again, if a housewife has bought ten loaves of bread at a 

 certain store and has found five of them not as fresh as might be 

 desired, she decides that in the future she will buy her bread elsewhere. 

 Both of these conclusions are based on an intuitive application of 

 sampling theory. Such examples could be multiplied indefinitely. 



Similarly, in most engineering problems, observational data are 

 involved in one way or another. In order to be able to assign 

 the proper significance to these data, it is essential to have some 

 idea as to their reliability, that is, to what extent they represent all 

 the facts under consideration. First, the measurements themselves 

 may be in error. In the second place, although the observations 

 may have been made with perfect precision, they may be incomplete; 

 they may constitute but a "sample" of a large group of possible 

 observations. The problem considered in this paper is one of this 

 second class, generally known as "sampling" problems. 



Assume the existence of a total group or "universe" of N objects 

 and that observations have been made on a certain number n of 

 them with reference to a particular characteristic. This number n 

 we will call the "sample." From this sample we wish to deduce 

 some estimate concerning the probable condition of that universe 

 with reference to the characteristic observed. 



Now the characteristic observed may itself take on one of two 

 forms. It may be either, (1) present or absent; (2) quantitative. 

 For simplicity in discussion we may call the first, "Sampling of 

 Attributes," and the second, "Sampling of Variables." 



An example of each will be cited from the telephone field. 



Example 1 : Sampling of Attributes 



Suppose that 4,000 relays of a particular type constitute a day's 



output. In order to determine roughly what proportion of these are 



non-operative at a current of 12 mils, a sample of 500 relays is tested 



and out of this sample 10 fail to operate at the required current. In 



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