11nov2000; cross-references corrected 28nov2000

Soc210a, McFarland


Assignment 8.  Logic of Statistical Inference


1. After reading Moore and McCabe Section 6.2, Tests of
Significance, do the following problems beginning on page 468:
        6.27, 6.35, 6.37, 6.43

2. After reading Moore and McCabe Section 6.3, Uses and Abuses of
Tests, do the following problems beginning on page 481:
        6.55, 6.57

3. After reading Moore and McCabe Section 6.4, on Power, Error
Types and Error Probabilities (omitting Inference as a Decision),
do the following problems beginning on page 493:
        6.63, 6.69, 6.76; 6.81, 6.82

4. After reading Moore and McCabe Section 7.1, Inference for a
Population Mean, do the following problems beginning on page 523:
        7.1, 7.3 (omit part f), 7.15, 7.39

5.  After reading Moore and McCabe Section 8.1, Inference for a
Single Proportion, do the following problems beginning on page
596:
        8.1, 8.13, 8.14

Redo 8.13 and 8.14 assuming a design effect of 1.5, rather than a
SRS with design effect of 1.0.
  

6. (Refer to the binomial probability table you had stata
construct for you in Assignment 7, #2.) 

        (a) In n=10 trials, with p=.5, what critical region would
cut off approximately 5% of the probability in the upper tail of
the binomial distribution?  

        (b) If the event in question occurred on 8 of the 10
trials, would the null hypothesis be acccepted or rejected?
        
        (c) How could you go about finding the power of that test
against an alternative hypothesis that p=.7 instead of .5?  (How
would you modify the stata commands that you used to generate
the table for .5? And which entries of the resulting table would
figure in this power calculation?)


7.  A variable has a sample mean of 13 and sample standard
deviation of 5.  The standard error of the sample mean can be
estimated (12.20) from sample data, but it also depends on sample
size.  Calculate
       
        (a) estimated standard error of sample mean, if sample
size is 100.
                
        (b) estimated standard error of sample mean, if sample
size is 2,500.

        (c) 95% confidence interval for population mean, if
sample size is 100.
        
        (d) 95% confidence interval for population mean, if
sample size is 2,500.


8.  Use the educ variable in Hamilton's vttown.dta dataset.

        (a) Note the sample size.

        (b) Test the null hypothesis that the mean educ value in
the entire population of that town is 13.0 years:
                ttest educ = 13
Stata reports a significance probability; is that for a one-sided 
or two-sided test?

        (c) Find the 95% confidence interval for the mean educ
value in the entire population of that town:
                ci educ , level(95)

        (d) What difference would it make in the width of the
interval, if you used 90% instead of 95%? What about 99%?          

        (e) Compare these results with those of (7a) and (7c)
above.


9. Repeat (8a) through (8d), but this time using the educ
variable in the 1994 General Social Survey, rather than the one
in Hamilton's survey of a small Vermont town.

        (e) Compare these results with those of (7b) and (7d)
above.