Sec. 6.4 



TEST OF HYPOTHESIS H (fi = M ) 



173 



It will be assumed herein that the following test scores were made under the 

 two methods: 





What conclusions can we draw validly from these results? 



In the usual manner it is found that x = 5.65 in favor of A, and 

 that s £ = 0.87. Therefore, t = (5.65 - /0/0.87, with 19 degrees of 

 freedom. What is a reasonable hypothesis regarding the magnitude 

 of n in the population of X{ = A{ — B{ assumed to follow a normal 

 distribution? The purpose of this study was to determine if one 

 method of instruction is better than the other, and, perhaps, assess 

 the magnitude of the difference if one exists. If one method is superior 

 to the other, /z is not equal to zero; however, there appears to be no 

 logical way to decide ahead of the test just what the size of /x might be. 

 The problem therefore is attack by assuming that n = and then de- 

 termining statistically just how satisfactory such a hypothesis is. 



If n = 0, t = (5.65 - 0)/0.87 = 6.49, with 19 degrees of freedom. 

 It is clear from Table IV that a i of this size is an extremely rare 

 occurrence, a fact which leads us to reject decisively the hypothesis 

 that ju. = 0. In other words, method A most certainly is some better 

 than method B. If there is any benefit to be derived from an estimate 



