A software development company releases an upgrade to an existing
product with a radically new interface. They justify the new
interface by claiming increased productivity for all users and in
particular novices. They support this by citing a report that
states that novice users make 20 errors on average for a widely
used suite of tasks. An independent testing organization believes 
that this claim is optimistic and that novices make more errors on
this task suite than claimed. They decide to conduct an experiment to
investigate.

1. Give the appropriate null and one-sided research hypotheses.
 
   Solution: 
  
   H0: mu(y)=20 
   Ha: mu(y)>20 
 
 
2. The testing organization selects a random sample of 16 novice
   users and discovers that the mean error count is 24 with a 
   standard deviation of 9. Conduct a test of hypotheses.

   Solution: 
  
   we start with step 2 since step 1 is answered above:

   STEP 2 a) n=16, ybar=24, s(y)=9
          b) ybar=24 > 20 and so ybar is consistent with Ha

   STEP 3 a) mu(y)=20
          b) Since n=16 is small, then we must assume that error 
             count is normally distributed in order to proceed. 

             mu(ybar)=mu(y)=20
             s(ybar)=9/sqrt(16)=2.25.
             t=(24-20)/2.25=1.78. 
 
             From the t-table, for 15 df, the p-value is the 
             proportion to the right of 1.78 which is between 2.5%
             and 5% or, expressed as a probability, between 0.025
             and 0.05. 
 
   STEP 4. The p-value obtained is significant and so we have
           evidence to reject H0 and challenge the vendors claim.