Biostatistics 1 Fall 2005 Homework 8 due Nov 3 in lab

 Problem 1

    The National Center for Health Statistics gave the following data
    on the distribution of suicides in the U.S. by month in 1990. Is there
    any evidence that the suicide rate varies monthly, or are the data
    consistent with the hypothesis that the rate is constant?

    To simplify your analysis, assume the months have the same numbers of
    days. Compare the observed proportions across months qualitatively
    and through a formal goodness-of-fit test.  Write a short and coherent 
    summary to this problem.


         Month  Number of Suicides
         ----------------------
            Jan        1867
            Feb        1789
            Mar        1944
            Apr        2094
            May        2097
           June        1981
           July        1887
            Aug        2024
           Sept        1928
            Oct        2032
            Nov        1978
            Dec        1859


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 Problem 2:

   A study published in 1969 was conducted to investigate the effect of
   the duration of pre-natal care and the place where that care is
   received on the survival of infants.  The duration of care is classified
   as less than one month or at least one month. In our analysis we will
   look at the overall results, ignoring clinics.  The results of
   the study are summarized in the table below:


                          Duration of pre-natal care  
  Status of infant one 
  month after birth        < 1 Month   at least 1 month

           DEAD               20             6 
           ALIVE             373           316  

  Is there a difference in the death rate for infants whose mothers
  had less than one month of pre-natal care as compared with infants
  whose mothers had at least one month of pre-natal care?

  To answer the question, do the following:

  a. Conduct an hypothesis test for differences between two binomial
     proportions. Clearly state populations, parameters, hypotheses and
     conclusion (and clearly show what you used to get to the conclusion).

  b. Construct a 95% confidence interval for the difference of two binomial
     proportions.  Clearly interpret this interval. 



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  Problem 3:

    There are four major blood groups in humans: O, A, B, and AB. A sample
    of individuals with records at the Blood Bank of Hawaii was selected.
    Each individual was classified according to blood type and ethnicity.
    The following two-way table of counts was obtained.

      Blood Type                         Ethnicity

                    Hawaiian   Hawaiian-White   Hawaiian-Chinese   White
                    ----------------------------------------------------
         O            1903          4469             2206          53759
         A            2490          4671             2368          50008
         B             178           606              568          16252
        AB              99           236              243           5001



    a. Summarize these data, focusing on descriptive and graphical
       comparisons of the 4 ethnic groups on the proportions in the 4 blood
       groups. You should make a bar graph showing the distribution of blood 
       type for each of the ethnic groups (make sure you use proportions,not
       counts).  Graph > Bar Chart > Values from a table > Cluster 
       does a nice job of this.

    b. Is there evidence that blood type and ethnicity are associated
       in Hawaii? Explain.

    c. Carry out any additional analyses that you deem relevant, and
       summarize your findings. This is open ended. For example, you
       might consider comparing all pairs of ethnicities on blood types,
       to see which differ.