6nov2000


Soc210a, McFarland


Assignment 7:  Sampling Distributions and Estimation


1.  After reading Moore and McCabe, section 5.1 "Sampling
Distributions for Counts and Proportions", work the following
exercises beginning on page 390:

        5.1, 5.5, 5.7, 5.9, 5.11*, 5.19, 5.23

* (In 5.11, assume the sample is randomly selected from a list of
the employees of a particular large firm, and that the 25% figure
applies to the particular firm. Nobody has a list of all employed
women in the country from which to select a sample.)


2.  Use stata to construct a table of the binomial probability
distribution for n=10, p=.5, as follows:
        clear
        set obs 11
        generate unity = 1
        generate k = sum(unity)-1
        generate Patleast = Binomial(10,k,.5)
        generate kplus1 = k+1
        generate Pmore = Binomial(10,kplus1,.5)
        generate Pexactly = Patleast - Pmore
        list

3.  A previous assignment contained the following question:

        Sketch how one would answer the following, but do 
        not attempt the calculations yet. If p(female) is .5 
        in some remote village, what is the probability that 
        the next 100 births will have unequal numbers of male 
        and females?  

Review how you set it up, and now work out a numerical answer,
using the normal approximation to the binomial distribution. Note
that the integer value 50 in a discrete distribution, such as the
binomial, corresponds to the interval from 49.5 to 50.5 in a
continuous distribution, such as the Gaussian. Note also that the
textbook's tables are for the STANDARD Gaussian "normal"
distribution, so numbers such as 49.5 and 50.5 must be
standardized, by subtracting the mean and dividing by the
standard deviation, before consulting the tables.


4 (continuation).  Use stata to calculate the probability of
exactly 50 females in 100 births, with p=.5.
        clear
        set obs 1
        generate P50 = Binomial(100,50,.5) - Binomial(100,51,.5)
        list
Use the result for an alternative calculation for the probability
of unequal numbers of males and females.  How close are this
result and the approximation obtained in problem #3?


5.  After reading Moore and McCabe, section 5.2, "The Sampling
Distribution of a Sample Mean", do the following exercises:

        -beginning on page 408:  5.25, 5.39, 5.45
        -beginning on page 428:  5.63, 5.69


6.  After reading Moore and McCabe, section 6.1, "Estimating with
Confidence", do the following exercises beginning on page 447.
        
        6.1, 6.7. 6.10, 6.15, 6.17, 6.23