Stat 427/527 Homework 2 due Thursday September 22, 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.


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1. The data (on the course page) were collected in southern Florida between 1968 and 1972 to 
   test a hypothesis that massive injection of silver iodide into cumulus clouds can lead to 
   increased rainfall.  On each of 52 days that were deemed suitable for cloud seeding, a random 
   mechanism was used to decide whether to seed the target cloud that day or to leave it unseeded 
   as a control.  An airplane flew through the cloud in both cases, since the experimenters and the 
   pilot were themselves unaware of whether on any particular day the seeding mechanism in the plane 
   was loaded or not (that is, they were blind to the treatment).  Precipitation was measured as the 
   total rain volume falling from the cloud base following the airplane seeding run, as measured by 
   radar.  

  a. Obtain histograms and boxplots of seeded and unseeded days.  Describe the distributions. 
     Why is this shape almost certain to occur here?

  b. Obtain 95% confidence intervals for the mean precipitation amounts of each group.  
     Do they overlap?  Do the assumptions for the method appear to be appropriate?  Discuss.

  c. Transform the data by taking the log of each value.  Make histograms and boxplots of the 
     transformed data.  Describe the distributions of the transformed data.

  d. Repeat part b for the transformed data.


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2. The following data are the total cholesterol levels (TCL) for a sample of 14 young adult males 
   (aged 25 years or less) on the Kaiser Health plan in California:


        227   239   221   213   218   246   218   224   210   204   197   229   220   197
 

   Suppose it is believed that the mean TCL of all adult males in the United States is 210. Is it 
   plausible the (population) mean TCL of all young adult males on the Kaiser plan is the same as the 
   U.S. male population mean TCL? Test at the 5% level. Be sure to state any assumptions needed to 
   carry out the test and check whether these assumptions are reasonable. Also, construct and 
   interpret a 95% CI for the Kaiser population mean.

   Note that this problem involves two populations, one of which is a subset of the other. 
   Furthermore, we are assuming that the mean for the larger population is known - This is a 
   one-sample problem because only 1 sample was taken.

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3. If you follow the path File > Open Worksheet in Minitab, you will see a worksheet named Acid.  
   Load it.  In C1 are the results of a titration to determine the acidity of a solution in a 
   chemistry class.  In C2 are the results from a second experiment.

   The instructor knew in both cases that the correct value for this solution was 0.110.  
   Use a test of hypothesis and corresponding CIs to see if the class is “biased” – that is, to see 
   if the class is systematically too high or too low.  Do this for both experiments.  Be sure 
   to state and check all assumptions.