UCSC SS2 2020
Aaron G Meininger
Wage Experience CollGrad
11 2 1
4 3 0
14 7 0
12 3 1
24 15 0
6 4 0
1. Use the sample student data above to compute the following descriptive
statistics. You may use a calculator but must show all your work.
What are the mean, variance, and standard deviation of wages?
What are the mean, variance, and standard deviation of experience?
What are the mean, variance, and standard deviation of College
Create a scatter plot with experience on the horizontal axis and wages
on the vertical axis. Without calculating it, draw a straight line that
best fits the data points. Does the relationship between wages and
experience appear to be positive or negative?
What is the covariance of wages and experience? Is this consistent
with your linear relationship?
What is the correlation between wages and experience?
Will covariance and correlation always have the same sign? Explain.
2. This question examines the hypothesis,”Does being a college graduate increase wages?” Continue to use the data above.
Does the data suggest that graduating increases or decreases your
wages? Carefully justify your answer while taking into account the
idea of ceteris paribus.
What is the covariance of wages and CollGrad? What does this
suggest about the relationship between wages and graduating from
Are your two answers consistant? Explain.
3. We will now change the scale of one of the variables. Continue to use the
wage data above.
Convert wages in the table above to euros rather than dollars (assume
one euro is worth 1.06125 dollars). Compute the mean and variance
What is the relationship between the mean and variance of wages in
this question and the mean and variance of wages found in the first
question. Be precise about your answer.
4. Prove using maths that the Cov(aX,bY) = abCov(X,Y) using the properties of summation. Show each step.
5. The National Cellular Networks Association wishes to estimate the average
number of cellular phones owned by U.S. households. They are considering
two methods of sampling. For each method, explain if you think it will be
subject to selection bias and why, and if you think it will be subject to
non-response bias and why. Also, state whether you think each method
will result in too small or too large an estimate of the true household
The Association will call a random sample of phone numbers in every
phonebook during regular business hours and ask how many cellular
phones the household owns.
The Association will survey people at the entrance of each ComicCon
in the United States between the months of June and August.
Now propose a sampling method of your own that you think will
generate a more accurate national average. Explain why you think
it is better.