CORRECTION OF DATA FOR ERRORS 317 



Solnlio)!: 



If n is small, wc proceed as in the previous case, to find the proba- 

 bility of occurrence of the obser\ed difference. If this probability is 

 small, we conclude that the difference is significant; i.e., the two 

 methods of preservation gi\e different results. 



Example 3: 



Three-bolt guy clamps are used for clamping the guy wires on tele- 

 phone poles. These are supplied from different sources. Those from 

 one source fail to hold the wire as well as those from another and in- 

 spection shows that these same clamps fail to meet a certain specified 

 dimension. The force required to slip the wire in each of 10 clamps 

 from this source is measured. These clamps are then modified to 

 meet the specified dimension and the force required to slip the wire 

 in each clamp is again measured. Are we justified in attributing the 

 failure to hold the wire to the fact that these clamps did not meet 

 the specificati(Mi.-' 



Solution : 



The solution follows the same line as in the first case. 



Discussion of Problems of Type 2: 



Problems of this type are very numerous. It is obvious that sig- 

 nificant differences calculated as above indicated are always larger 

 than those calculated by customary theory. 



Problem Type 3, Determination of Most Probable Value of the 



Root Mean Square Deviation of the Universe When 



Only One .Sample of n Pieces Has Been Examined 



Example 1 : 



Five tool-made models are tested for their efficiency, giving values 

 Xi, Xo, ... X5. What is the most probable \-alue of the range within 

 W'hich the efficiencies of product instruments may be expected to lie 

 approximately 99.7% of the time, assuming that a manufacturing 

 process can be developed which is the same as that used in producmg 

 the tool-made models? 



