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ECON 471: Econometrics

Problem Set #1

Due February 14, 2022

1. You are tasked with evaluating if there is a difference in the average wages of college

graduates and non-college graduates. You take a random sample of 1,600 college

graduates and a random sample of 2,700 non-college graduates. The average wage in

your sample of graduates is $35/hour, with a sample standard deviation of $40/hour. The

average wage in your sample of non-graduates is $31/hour, with a standard deviation of

$90/hour.

a. What are your null and alternative hypotheses?

b. State your conclusion regarding the difference in average wages, using 5%

significance.

c. What is the 95% confidence interval for the difference in average wages?

2. You collect two random samples, one for males and one for females, and calculate the

average number of hours worked in each sample. You find a difference in the average

number of hours worked of 5 hours/week. Furthermore, based on the data, you reject the

null hypothesis that the average number of hours worked for males and females are equal

at 5% significance. Can you conclude that being female causes individuals to work fewer

hours per week? Why or why not?

3. The final price a consumer pays for a six-pack of soda is dependent on the posted price

and sales tax. In San Marcos, sales tax is 8.00%. The average posted price for a six-pack

of soda in San Marcos is $4.99. The variance of the posted price for a six-pack of soda in

San Marcos is 3.50. What are the average final price and the standard deviation of the

final price paid for a six-pack of soda in San Marcos?

4. Use the Earnings and Height data on Cougar Courses to answer the following questions.

a. What are the sample average, and standard error of the sample average for

earnings?

b. What proportion of the individuals in the data are female?

c. What proportion of the individuals in the data are black males?

d. Are the average earnings in the population different than $46,000?

e. Do males earn more than females?

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Econometrics

Standard cost

Average final price

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