A manufacturer of workstations claims that a new workstation
achieves a score of 200 on the Tower of Hanoi benchmark. An
independent testing organization disputes this claim and
believes that the workstation is slower than claimed.

Note:	The Tower of Hanoi (TOH) benchmark score is the number 
	of TOH moves made in 25 microseconds.

1. Give the appropriate null and one-sided research hypotheses
   that correspond to the testing organizations point of view.
   
   H0: mu(y)=200 
   Ha: mu(y)<200 
 
 
2. The testing organization selects a random sample of 16
   workstations and discovers that the mean benchmark score is
   199 with a standard deviation of 2.5.

   a) Compute the test statistic for your hypotheses. Make and
      state any necessary assumptions.
 
      Since the sample is small, we must assume that benchmark
      score is normally distributed. If so, ybar is Student t
      distributed with 15 df and:
                 mu(ybar)=mu(y)=200 
                 s(ybar)=2.5/sqrt(16)=0.625.
      The test statistic t is:
                 t=(199-200)/0.625=-1.6 
 
   b) Determine the p-value. 
 
      From the t-table, for 15 df, the proportion to the right 
      of 1.6 is between 5% and 10%. By symmetry, this is also
      the proportion to the left of -1.6 which is the desired
      proportion.
 
   c) Given the p-value obtained comment on the manufacturers claim.

      This is non-significant and so we have insufficient evidence
      to challenge the manufacturers claim.