Department of Economics Professor Siegler

Homework Essay Help: Economics 102

Problem Set #2 Key

20 points possible

Due in SmartSite on Sunday, January 25 by 10 p.m.

Department of Economics Professor Siegler

UC Davis Winter 2015

Instructions: Please submit a self-contained and well-formatted Word (or similar) document in

SmartSite containing all of your written answers, calculations, and graphs to the seven questions

below. Also, submit Excel and GRETL documents containing the background calculations and

graphs used in Word. Remember that the problem set will be graded, in part, based on the

visual presentation of your results.

1. The Normal and Standard Normal Distributions (3 points)

Professor Economises has 362 students in her introductory economics class. Suppose

that the scores on the final exam in this class are normally distributed with a mean of 75

points and a standard deviation of 10 points. How many students in the class can be

expected to receive below 60 points? Convert the distribution to a standard normal

distribution and express your answer to the nearest number of students. Show your work

and explain. 

2. Monte Carlo Simulation and the Central Limit Theorem in Excel (4 points)

Suppose that a hot dog factory is attempting to produce foot-long hotdogs 12 inches in

length. There is variation in the process, however, and the actual lengths of the “footlong”

hotdogs vary uniformly between 11.5 and 12.5 inches in length. At regular

intervals, a random sample of 10 hotdogs is selected, the lengths measured, and the

average (mean) length of the ten hotdogs is recorded. After 500 samples of 10 hotdogs

have been selected, the frequency distribution of the 500 sample means is plotted (the

sampling distribution of the mean). Even though the data generating process (DGP) is a

random uniform distribution and the sample size (n=10) is small, the distribution of

average lengths tends toward the normal distribution. This Monte Carlo simulation

should provide intuition regarding the Central Limit Theorem (CLT). Please follow the

steps below to conduct this Monte Carlo simulation.

3. Applying the Central Limit Theorem (3 points)

A nationwide study found that the average yearly claim per automobile insurance policy

(after deductible) is $500 with a standard deviation of $2,500. Consider these parameter

values to be the true population parameters.

Suppose that you are working for a small, start-up insurance company with only 10,000

automobile insurance policies, and the company has $4.5 million to pay for claims next

year. What is the probability that the company will not have enough money set aside to

pay off the claims next year? If the company does not have enough money set aside, it

will declare bankruptcy and you will lose your job. Should you start working on your

resume? Show your work and explain. 

4. Hypothesis Testing by Hand (4 points)

Consider the number of days absent from a random sample of seven students during a

quarter in a large introductory economics class.

= -0, 1, 1, 3, 3, 8, 12.

Can you reject the null hypothesis that the population mean number of absences in this

large introductory economics class is 8 at the ten-percent level of significance, at the 5-

percent level of significance? Use the critical value approach. You can use GRETL for

critical values, but you must show all of your calculations, using Equation Editor in

Word, and explain. 

5. Spending on Textbooks and Course Materials (3 points)

Recently, it was claimed that college students spend an average of $1,200 per year on

textbooks and course materials (see Ethan Senack, Fixing the Broken Textbook Market,

January 2014, http://www.uspirg.org/reports/usp/fixing-broken-textbook-market).

Assuming that the attached file (textbook.xls) is a random, representative sample of

college students (n=84), where each row in the spreadsheet represents one student’s

response, measured in dollars. Can you reject the null hypothesis that the average college

student spends $1,200 a year on textbooks at the one-percent (0.01) level of significance?

Show your work and explain using the critical value, p-value, and confidence interval

approaches. Be sure to intuitively explain what your results imply. Use GRETL for

this question.

6. Testing Proportions (3 points)

Suppose someone claims that at least 90 percent of U.S. households have internet access.

To test this claim, you randomly sample 100 U.S. households and find that 81 percent of

your sample has internet access. What are the null and alternative hypotheses? What is

the value of your test statistic? Can you reject the null hypothesis at the five-percent

level of significance? Can you reject the null hypothesis at the one-percent level of

significance? Show your work and explain. 

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