Elements of Statistics (Math 6) - Exam 1 Name
September 25, 1998 - Hartlaub

Directions: Please answer all of the questions below. The point values for each problem are indicated in parentheses. Partial credit will be awarded if you show your work.

1.  Describe the relationship between the mean and the median if the distribution of the data is

symmetric (3 points)
skewed to the right (3 points)
skewed to the left (3 points)

2.  A college newspaper interviews a psychologist about a proposed system for rating the teaching ability of faculty members. The psychologist says, "the evidence indicates that the correlation between a faculty member's research productivity and teaching rating is close to zero." A correct interpretation of this statement would be (5 points)

a.  good researchers tend to be poor teachers and vice versa.
b.  good teachers tend to be poor researchers and vice versa.
c.  good researchers are just as likely to be good teachers as they are bad teachers. Likewise for poor researchers.
d.  good research and good teaching go hand in hand.

3.  Suppose that the average salary of all female workers is $35,000 and the average salary of all male workers is $41,000. What must be true about the average salary of all workers? (5 points)

a.  It must be $38,000.
b.  It must be larger than the median salary.
c.  It could be any number between $35,000 and $41,000.
d.  It must be larger than $38,000.

6.  Suppose that the time taken for a computer on a local area network to establish a connection to a remote site follows the normal distribution with a mean of 15 seconds and a standard deviation of 3 seconds. (25 points, 5 points for each part)

a.  What proportion of the connections will occur in less than 12.2 seconds?
b.  What proportion of the connections will occur between 12.2 and 16.5 seconds?
c.  What proportion of the connections will take longer than 10 seconds to establish?
d.  90% of the connections will occur in less than how many seconds?
e.  75% of the connections will take longer than how many seconds to establish?

7. The file p:\data\math\stats\pines97.mtw contains measurements on pine trees planted in 1990 at the Kenyon Center for Environmental Studies. Retrieve the file and answer the following questions. (45 points, 5 points for each part)

a. Is the distribution of leader growth during 1996 (grow96) symmetric or skewed? If skewed, in what direction?
b. Provide two measures of center for the distribution of heights at planting time (hgt90).
c.  Provide two measures of variability for the distribution of heights at planting time (hgt90).
d.  The heights at planting time (hgt90) were recorded in centimeters. Explain how you would standardize the heights so that they have a mean of 0 and a standard deviation of 1.
e.  Construct a normal probability plot for the tree heights in 1997 (hgt97). Do you think the normal model is appropriate for these heights? Explain.
f.  Is there any association between needle length (needles97) and tree diameter (diam97)?
g.  Find the least squares line for predicting tree height in 1997 (hgt97) from tree diameter in 1997 (diam97).
h.  What percentage of the variation in tree heights did you explain by using tree diameters to fit the least squares line?
i.  Plot the residuals against the fitted values. What does the plot tell you about the adequacy of the linear fit?