Statistics: How to determine Ho and Ha?

Question

Does the princeton Review improve SAT scores? Five students were SRS and asked to participate in the experiment. Their SAT scores were recorded before the review and after the review.

 

Person:          1         2          3       4         5

score after:   990     1000    890    980       1020

score before: 980      980    920    970        1000

 

Is there sufficient evidence at the 5% significance level to indicate that the Princeton review helps increase a student's SAT score?

 

-----------------------------------------

I have trouble discerning the different Ho's and Ha's found in problems, one problem would be like Ho: mu=0 Ha: mu>0

and another would be Ho: u=0 Ha: u>0  

 How do I figure out what to put in the Ho and Ha? 

 

Thanks

 

 

Answer 1

Your two examples for H₀ and H_a seem to be the same.

 

But in any case two possibilities H₀:mu=0   H_a:mu≠0   and   H₀:mu=0  H_a:mu>0

 

If this is what you meant then your choice depends on the way the question is worded.

 

In the question you gave as an example the question asks about an "increase" so the hypotheses you would use is the second pair.

 

If the question just asks has there been a change then it is the first pair.