Sec. 5.3 PREDETERMINED HYPOTHESES REGARDING p 133 



X 2 got so large as this purely as the result of the chance occurrences 

 of sampling? As was done earlier, attention will be called first to 

 some actual sampling experiences, and then a mathematical table 

 will be employed to obtain the required information more quickly 

 and more accurately. Table 5.31 summarizes the results obtained 

 from 652 samples from a population for which p was known to be 1/2. 

 Figure 5.31 is the graph of the r.c.f. distribution presented in Table 

 5.31. 



TABLE 5.31 



Observed Frequency and r.c.f. Distributions for x 2 When the Two 

 Classes, Male and Female, Determine the Population, and p = 1/2 



.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 

 X 2 

 Figure 5.31. Sampling distribution of x 2 with one degree of freedom, as deter- 

 mined from 652 samples taken from a binomial population with p = 1/2. 



If we read upward from x 2 = 0.51 to the graph of Figure 5.31 and 

 then horizontally to the vertical scale, it appears that about 52 or 53 

 per cent of all such sampling values of x 2 would exceed 0.51. Ob- 

 viously, then, 0.51 is not an unusual sampling size for x 2 , provided 

 the hypothesis upon the basis of which the expected numbers were 

 calculated is exactly correct. Hence it is entirely reasonable to sup- 

 pose that this sample of male and female guinea pigs deviated from 



