Econ 113

UCSC SS2 2020

Aaron G Meininger

Assignment 1

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

Graduation (CollGrad)?

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.

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What is the covariance of wages and CollGrad? What does this

suggest about the relationship between wages and graduating from

college?

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

of wages.

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

average.

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.

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