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 studies that
state that novice users make 20 errors on average for a standard
task suite. An independent testing organization believes that
this claim is optimistic and that novices make more errors on
this task suite.

1. Give the appropriate null and one-sided research hypotheses
   that correspond to the testing organizations point of view.
   
   H0: mu=20 
   Ha: mu>20 
 
 
2. The testing organization selects a random sample of 26 novice
   users and discovers that the mean error count is 24 with a 
   standard deviation of 9.

   a) Compute the test statistic for your hypotheses. 
 
      Since the sample is small, s(ybar)=9/sqrt(25)=1.8.
      Since we assume H0 true, t=(24-20)/1.8=2.22. 
      Reminder: Since n is small, you must assume y normally
                distributed.
 
   b) Determine the p-value. 
 
      From the t-table, for 25 df, the p-value is the proportion
      to the right of 2.22 which is between 1% and 2.5% or,
      expressed as a probability, between 0.01 and 0.025. 
 
   c) Given the p-value obtained comment on the vendors claim.

      This is significant and so we have sufficient evidence
      to reject H0 and challenge the vendors claim.