176 SAMPLING NORMAL POPULATIONS Ch. 6 



6.5 A STATISTICAL TEST OF THE HYPOTHESIS THAT 



TWO SAMPLES OF OBSERVATIONS HAVE BEEN 



DRAWN FROM THE SAME NORMAL 



POPULATION OF NUMERICAL 



MEASUREMENTS 



If two samples have been taken under the same conditions but 

 with some one important feature changed, we usually wish to learn 

 if this change has produced a new population of measurements. For 

 example, if two groups of Duroc-Jersey pigs have been fed two dif- 

 ferent rations, the experimenter wants to know if the difference in 

 ration has produced an important difference in average daily gains. 

 That is, has the difference in ration created different populations of 

 average daily gains? Fundamentally, the method to be employed 

 in the solution of this problem is the same as that described in the 

 preceding section, but the mechanics of the procedure need to be 

 altered to fit the new sampling situation. 



The following symbols will be employed: 



di = xu — X2% = the difference between the ith. sample mean from 

 samples from group 1 and the corresponding sam- 

 ple from group 2, and 



St = the standard deviation of the d;. 



Before the general method for attacking the problem just posed is 

 described, some actual sampling experiences will be presented in tabu- 

 lar form, and discussed. Table 6.51 shows a summary of 403 d{ ob- 

 tained from pairs of samples, each with n = 10 drawn from the near- 

 normal population of Table 6.21. It is recalled that the standard 

 deviation of that population is a = 10. 



TABLE 6.51 



Frequency and r.c.f. Distributions for 403 Sample Values of di with 

 n = 10 Drawn from a Near-Normal Population with /x = 60 and a = 10 



Arithmetic mean of di — +0.06; standard deviation = 4.43. 



