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.

ˆ What are the mean, variance, and standard deviation of wages?

ˆ What are the mean, variance, and standard deviation of experience?

ˆ What are the mean, variance, and standard deviation of College Graduation (CollGrad)?

ˆ 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?

ˆ What is the covariance of wages and experience? Is this consistent with your linear relationship?

ˆ What is the correlation between wages and experience?

ˆ Will covariance and correlation always have the same sign? Explain.

2. This question examines the hypothesis,”Does being a college graduate in- crease wages?” Continue to use the data above.

ˆ 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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ˆ What is the covariance of wages and CollGrad? What does this suggest about the relationship between wages and graduating from college?

ˆ 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.

ˆ 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.

ˆ 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 proper- ties 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.

ˆ 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.

ˆ The Association will survey people at the entrance of each ComicCon in the United States between the months of June and August.

ˆ 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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