Tools of Economic Analysis
1. Use the accompanying dataset (found in the problem set folder on blackboard, file name "Problem set 1 data.xlsx") to answer this question. Use the worksheet labeled "Question 1". The data were acquired through the Federal Reserve Economic Database (https://fred.stlouisfed.org/).
a) Calculate the mean value of the two indexes between December 2014 and September 2016.
Average, December 2014 to September 2016, DJIA (rounded to 3 decimal places): _______
Average, December 2014 to September 2016, S&P 500 (rounded to 3 decimal places):_______
b) Calculate the variance and standard deviation of the two indexes between December 2014 and September 2016. Use the sample variance and sample standard deviation formulas in Excel.
Variance, DJIA, December 2014 through September 2016 (rounded to 3 decimal places): ______
Standard deviation, DJIA, December 2014 through September 2016 (rounded to 3 decimal places): ____
Variance, S&P 500, December 2014 through September 2016 (rounded to 3 decimal places): ________
Standard deviation, S&P 500, December 2014 through September 2016 (rounded to 3 decimal places): ______
c) Calculate the coefficient of variation for each index and compare (hint: see Lecture 1 slides for a definition of "coefficient of variation"). Which index is more volatile? Is your answer consistent with a comparison of the sample variance of the two indexes? Why or why not?
2. Consider the contingency table below, based on a random sample, and answer the following questions.
|
Table A: Employment Statistics
|
|
|
Employed
|
Unemployed
|
Total
|
|
Male
|
200
|
40
|
240
|
|
Female
|
180
|
36
|
216
|
|
Total
|
380
|
76
|
456
|
a) What is the male unemployment rate? What is the female unemployment rate? (Hint: calculate Pr(Male AND Unemployed), Pr(Female AND Unemployed).)
b) What is the probability of unemployment conditional on being male? What is the probability of unemployment conditional on being female? (Hint: calculate Pr(unemployed | male), Pr(unemployed | female).)
c) Are unemployment status and sex independent events in this case? Why or why not? (Hint: recall that two events A, B are independent if Pr(A | B) = Pr(A).)
3. Using the accompanying data set to answer this question ("Problem Set 1 data"). Use the worksheet labeled "Question 3". The wage data are from a random sample of a classroom.
a) Calculate the mean and median wage and round your answer to 3 decimal places
b) Calculate the sample standard deviation and round to 3 decimal places
c) Describe the data in a few sentences. Are the data bell-shaped? Skewed left or right? Explain how you came to your conclusions.
4. Answer the following questions based on the standard normal distribution (i.e., a normal distribution with mean zero and standard deviation equal to 1). For full credit, report your answer AND the Excel formula you used.
a) Calculate the area to the left of z=1.34:
b) Calculate the area between z=0.75 and z=1.5:
c) Find X such that Pr(z<-X) + Pr(z>X) = 0.10: