Lab assignment 6 (due Wednesday, March 22)

*** SLBD stands for the book "Statistics: Learning by Doing."  ***

*** SAWA stands for "Short Answer Writing Assignment"  ***

Please read lab session 9 (pages 122-138 of SLBD) BEFORE coming to class
on Monday.

This lab session will follow closely the one described in SLBD, so be sure to 
have read it.

I.  Answer SAWA questions 1-6 on pages 139-140 of SLBD, in complete sentences 
where possible.  Also turn in a completed copy of Table 9.1.

Notation:  For example, a^2 denotes "a squared" in the following questions.

II.  Statistical theory can be used to show that for large samples for a NORMAL 
population, the VARIANCE of the sampling distribution of the sample 
MEDIAN is approximately (pi/2)*(sigma^2/n).  Calculate this variance for sigma=1 
and n=20.  How does this compare with your simulated results?  [Look at the square 
of the standard deviation for your set of sample medians from the standard normal 
data with n=20.  This should be written in your Table 9.1 of the lab book.] 

III.  The standard double exponential distribution is a symmetric distribution 
centered at zero.  (Its density curve looks a bit like the exponential 
density on p. 124 of SLBD if you drew a mirror image of that density on the left 
side of zero.)  
       Statistical theory says that for large samples from the double exponential 
distribution, the variance of the sample mean's sampling distribution is 
2*(beta^2)/n and the variance of the sample median's sampling distribution is 
(beta^2)/n, where beta is simply a parameter (some number).  (Both of 
those sampling distributions have mean zero.)  
       Based on this result, if you knew your data had a double exponential 
distribution and you planned to take a large sample, which measure of 
central tendency would you prefer, the sample mean or sample median?  Why?