ECON 83a: Statistics for Economic Analysis
Problem Set #2, Spring 2021
1. The following data show the yearly salaries of football coaches at some state supported universities.
University Salary (in $1,000)
A 53
B 44
C 68
D 47
E 62
F 59
G 53
H 94
For the above sample, determine the following measures:
a. The mean yearly salary.
b. The range.
c. The variance.
d. The standard deviation.
e. The coefficient of variation.
2. Assume that each of these coaches could as well move to Canada and earn the same salary in that country (subject to conversion to Canadian dollars). Also, as- sume that 1 U.S. dollar is equal to 1.30 Canadian dollars. Therefore, for example, the first coach would earn 68,900 Canadian dollars instead of 53,000 U.S. dollars. Using these guidelines, recalculate theyearly salary of each coach. Moreover:
a. Recalculate the mean yearly salary.
b. Recalculate the range.
c. Recalculate the variance.
d. Recalculate the standard deviation.
e. Recalculate the coefficient of variation.
f. Comment on your results. How did the change of scale affect these measures?
3. Further, assume that a coach who decides to move to Canada receives an addi- tional yearly relocation bonus of 5,000 Canadian dollars. Therefore, for example, the first coach would earn 73,900 Canadian dollars instead of 68,900 Canadian dol- lars (or 53,000 U.S. dollars). Using these guidelines, recalculate theyearly salary of each coach. Moreover:
a. Recalculate the mean yearly salary.
b. Recalculate the range.
c. Recalculate the variance.
d. Recalculate the standard deviation.
e. Recalculate the coefficient of variation.
f. Comment on your results. How did the change of scale affect these measures?
4. In a statistics class, the average grade on the final examination was 75 with a standard deviation of 5. Use Chebyshev’s theorem to answer the following ques- tions.
a. At least what percentage of the students received grades between 50 and 100?
b. Determine an interval for the grades that will be true for at least 70% of the stu- dents.
5. The following data represent the daily demand (yin thousands of units) and the unit price (x in dollars) for a product.
Daily Demand (y) Unit Price (x)
47 1
39 3
35 5
44 3
34 6
20 8
15 16
30 6
a. Compute and interpret the sample covariance for the above data.
b. Compute and interpret the sample correlation coefficient.
6. Consider a sample with the following data values.
462
490
350
294
574
a. Compute the standardized values for the above five observations.
7. As in the case of Problem Set #1, download Nobel .RData from LATTE. Again, open this data set in R Studio and update using the biographical information about Paul Milgrom and Robert B. Wilson. Also, create a new variable, called Age, which records an individual’s age at which he or she received the award.
a. Calculate the range of age at award. (Use commands called min and max.)
b. Calculate the interquartile range of age at award. (Use – twice – a command called quantile, also selecting appropriate options.)
c. Calculate the variance of age at award. (Use a command called var.)
d. Calculate the standard deviation of age at award. (Use a command called sd.)
e. Calculate the covariance of YOA and Age. (Use a command called cov.)
f. Calculate the correlation coefficient of YOA and Age. (Use a command called cor.)
Comment on the relationship between these two variables. What does it mean that these two variables are related in this specificway?
To receive full credit, submit both your answers to these questions and a printout of your commands and output from R Studio’s console.