). Up to this point, we have used nontechnical language, and talked about issues being "surprising" in terms of our "initial assumptions." These concepts have formal names in statistics.
Our initial assumption is called the null hypothesis.
The null hypothesis often reflects the assumption that there is no difference
between the mean of of a no-treatment population and the mean of the treatment
population from which the sample is drawn. In our example, the null hypothesis
assumes that the average score for the population of students who took the training
course is the same as the mean of the population that did not take the course.
Another way to state this is that the mean score of the population that took
the course is 555 (i.e., the same as the mean for people who didn't take the
course). ().
Another Example and Some Questions
For our second example, we are going to look at another GRE preparation course, Training Program B.
Training Program B is moderately expensive ($275 per course). The average score on the GRE quantitative section for graduates of this course is 625. Recall, the average score for people who took the GRE quantitative section with no training is 555 with a standard deviation of 139. We will draw several samples of 25 people from the population of students who participated in training course B.
If we were interested in testing whether Training Program B graduates score better than 555, what form would our null hypothesis take?
a) 
b) 
c) 
d) 