128 SAMPLING FROM BINOMIAL POPULATIONS Ch. 5 



Table 5.21a has been added to show, through the preceding discus- 

 sions, just how the numbers in Table 5.21 could be got. Obviously, 

 if n were as large as 50 the work illustrated above would become 

 tremendously laborious. 



In Table 5.21 the observed fraction, r/n, was used instead of r 

 because it was convenient to do so. 



TABLE 5.21a 



95 Per Cent Confidence Limits with n — 10 



r L U r L U r L U 



The use of Table 5.21 will be illustrated by some examples. 



Problem 5.21. Suppose that a random sample of 250 primers for cartridges 

 has been taken from a large batch and has been tested by actual firing. If 6 

 of the primers fail to fire, place a 99 per cent confidence interval on the true 

 percentage of duds in the whole batch, and interpret these limits. 



For this sample r/n = 6/250 = .024, which is so near to the value 

 of .025 listed in Table 5.21 that interpolation is unnecessary. There- 

 fore, the required confidence interval is read from the table as 1 to 6 

 per cent duds in the whole batch. If future action regarding these 

 primers is based on the assumption that at least 1 per cent but not 

 more than 6 per cent of them are duds, a risk of only 1 in 100 is 

 being run that the sample has been misleading. If 6 per cent is more 

 than the allowable proportion of duds, this sample indicates that the 

 batch may be substandard. Whether the primers would be rejected 

 or additional evidence obtained would depend upon the particular 

 circumstances. 



Problem 5.22. Suppose that a concern which manufactures roller bearings 

 must meet a standard of 95 per cent acceptable according to certain prescribed 

 measurements. If a sample of 250 yields 3 unacceptable bearings, is the ship- 

 ment up to the required standard or not? 



In this instance r/n = .012, so the 95 and 99 per cent confidence 

 intervals are found to be to 3, and to 4, respectively, by interpola- 

 tion in Table 5.21. Therefore we could conclude that the shipment 

 has less than 5 per cent unacceptable with considerable confidence 



