Stat 427/527 HW 7 and 8 - due November 10, 2005

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********** This HW is worth 20 points **********
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 As in all HW, make sure to carefully define all population parameters 
 (proportions), and clearly define any hypotheses that you test.

 1. A 1997 survey conducted by M.I.T. reported that 16% of the 1,014 adults
    surveyed would be willing to support tax hikes to find extra-terrestrials.
    Find a 95% CI for the proportion p of all adults that favor such a
    tax hike.

    Suppose it was known that in 1990 that the proportion of all adults
    willing to support tax hikes to find extra-terrestrials was 0.2. Is
    there evidence that the proportion of adults in 1997 willing to
    spring for tax hikes for this purpose has changed since 1990?
    Carry out a test to answer this question. Use alpha=.05.


 2. Dr. Bedrick was involved in a study that examined the extent of 
    side effects from using amphetamines to treat children with traumatic 
    brain injuries.  Prior information suggests that the probability of 
    major side effects is very small, so it is of interest to 
    estimate the maximum plausible value that the probability of 
    major side effects might be.  In the study 
    none of the 15 children had major side effects.

    a. Compute an exact upper 95% confidence bound 
       for the probability of major side effects.

    b. Write a short conclusion to your analysis, interpreting the results
       of the exact bound in the context of the problem.

    c. What happens when you have Minitab attempt to compute the bound
       based on the normal distribution (under [Options...]) ?


 3. 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



4. The rising tide of national and regional loyalties around the world
    has bearing on the survival of minority or secondary languages. The
    article ``Language Maintenance and Shift in a Breton and Welsh Sample,''
    (Word, 1983; p67-88) describes one of the first comparative studies
    in this area. A random sample of 86 Welsh bilingual adults yielded 76
    who spoke Welsh fluently, while another random sample of 77 bilingual
    adults from Brittany resulted in 57 who spoke Breton fluently. Both
    Welsh and Breton are southern Celtic in origin. Do these data
    support the conclusion that the true proportion of fluent speakers
    among Welsh bilingual adults differs from the corresponding proportion
    for Breton bilingual adults?

    To answer this question, carry out an appropriate test at the 5%
    level, and quantify the difference in population proportions using a
    95% CI.


 5. 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 comparisons of the
       proportions in the 4 blood categories across the 4 ethnic groups.

    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.