188 



SAMPLING NORMAL POPULATIONS 



Ch. 6 



TABLE 6.7 ID 



By Central Limit Theorem (if n is large enough) /xj = 15.37 



<r 2 2 = 10.29 



the ^-distribution as long as w is normally distributed with mean n, 

 and s is calculated as described earlier. Hence if w is a sample mean 

 drawn from a non-normal population which satisfies the few require- 

 ments of the Central Limit Theorem, and if n is large enough, the 

 ratio (w — p)/s can be considered quite accurately to follow a ^-dis- 

 tribution. Thereafter the methods introduced in this chapter for 

 estimating parameters and for testing hypotheses regarding parameters 

 become applicable. 



One word of warning is in order, however, before this subject is left. 

 In any particular sampling situation, the standard deviation, o^, needs 

 to be estimated from the sample. This is done by means of s s . What 

 happens to the quality of this estimate when the parent population is 

 radically non-normal? Under such circumstances the beginner is 

 advised to seek the advice of a statistician. 



