Education 161   Winter 2000
                    Assignment 4   Due March 7, 2000

Note data files are available in one of two locations:
path: /usr/class/ed161/[data file]
or using web-services at URL
http://www.stanford.edu/class/ed161/hw/[data file]



1. File bernoulli.dat contains the results of 240 iid Bernoulli
trials.  Each trial is recorded as '1' for a success, '0' as a
failure.  Give a point and interval estimate of the Pr(success).
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2. 
 The 2x2 table below cross-classifies level of education (rows)
and voting intention (columns).  Compute a measure of association
between these two variables and test whether the association is
different from zero.

                      Will Vote          Not Vote
      Some HS           1481               132


      No HS              1036               173

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3.
Most colleges and Universities have annual campaigns in which
they ask former graduates to contribute money.  For the 1986 to
1987 Providence College fund-raising campaign, statistics were
recorded for the number of people contacted and the number of
doners categorized by their class year.  Some of these data are
summarized in the rable below.  (data from Providence College
Fund Year Report 1986-7).

                                    Class
                        1961   1966   1971   1976   1981
Contributed              196    266    194    276    333
Did not Contribute       123    226    241    322    568

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Construct a null hypothesis that the probabilities of
contributing are the same for all these 5 classes.

Calculate a table of expected counts under the assumption
that this null hypothesis is true.

Construct a test statistic for this null hypothesis and
carry out a test of the null hypothesis using Type I error rate
.01.

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4. File rxc.dat  contains data on two categorical variables,
one with four levels and one with 5 levels.  Obtain row and
column percentages for the cross-classification of these data.
Test the null hypothesis that these two variables are
independent using the traditional chi-square statistic (eg MT).

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5. LOGISTIC REGRESSION: BINARY OUTCOMES

The board of directors of a professional association conducted a random
survey of 30 members to assess the effects of possible dues increases.
The binary outcome variable is 1 if the subject indicated that membership 
would not be renewed and 0 if renewed for the specified dues increase.
data are in dues.dat.

a. use ordinary least-squares or weighted least squares to obtain the 
fit for a straight-line relation of response to (i.e. predicted by) 
amount of dues increase.
b.what's the largest residual from that fit?
c.what's the estimated probability that members will not renew if dues
are increased by $40?
d. estimate the amount of dues increase for which 75% of the members
will not renew.

Use Minitab binary logistic (blog) or SAS PROC LOGIST 
(following the examples of the Minitab or SAS runs
for the programming example in course example files) 
to obtain the logistic fit for parts e,f

e. repeat parts b,c,d for the logistic response function.
f. what's the prob of nonrenewal for a zero dues increase under each model?