Stat 427/527 Homework 3 due Thursday September 29, 2005

Directions: Do all calculations in MINITAB. Use a word processor of your 
choice to write a report.  Insert computer text output and graphics to 
support what you are saying, but you need to write something that looks 
like an academic paper - not a pile of computer output.  Also,

a. Clearly define population parameters in each problem.  That is, give 
   a verbal description of what the population mean is in the context of 
   the problem.

b. Clearly specify hypotheses when appropriate (not every problem 
   involves a test of hypothesis).

c. Write a coherent conclusion based on each CI or test.



1. Return to the cloud seeding problem (problem 1) of Homework 2.  This
   really is a two-sample problem, although we analyzed it in HW 2 as two
   one-sample problems.  

   a.  Carefully check the assumption of normality on the original scale
       using normal scores plots, and both tests discussed in class for 
       a formal test of the normality assumption.  You need to do the 
       seeded and unseeded days separately.  Describe how this anlaysis
       fits with the description of distribution you did in HW 2.

   b.  Repeat part a for the transformed data.

   c.  Compare the groups using two-sample t-procedures.  Choose the most
       appropriate scale in which to perform this analysis.  How does this 
       analysis compare with what you found in HW 2?

2. Use the Acid data (problem 3 HW 2).  

   a.  Check the normality assumption for both experiments as in problem 
       1 above.

   b.  Formally compare the experiments using two-sample t-procedures.


3. Cyclic adenosine monophosphate (cAMP) is a substance that can mediate
   cellular response to hormones. In a study of maturation of egg cells
   in the frog Xenopts laevis, oocytes from each of four females were 
   divided into two batches: one batch was exposed to progesterone and
   the other was not. After two minutes, each batch was assayed for its 
   cAMP content, with the results given in the table below.

                    cAMP (pmol/oocyte)

            Frog     Control   Progesterone
           --------------------------------
             1        6.01       5.23
             2        2.28       1.21
             3        1.51       1.40
             4        2.12       1.38
           --------------------------------

   a.  Make a histogram and box plot of the differences 
       between the cAMP levels for the control and progesterone samples.

   b.  Test at the 10% level whether there is any difference in the 
       population mean cAMP levels for batches of oocytes that are
       untreated versus those treated with progesterone. 

   c.  Compute and interpret a 90% CI for the difference in population
       mean cAMP levels for batches of oocytes that are
       untreated versus those treated with progesterone.

   d.  Discuss any statistical assumptions that you have made in carrying
       out the analysis, and whether the assumptions seem reasonable.

   e. Write a short summary to the problem.