Problem Set 4
Econ 253

Problems from Textbook 3.14 (d), 3.16, 3.13 (a)

Additional Problems:

1. In order to estimate the mean monthly expenditures for food for a family of four living in Springfield, a random sample of fifty families was chosen. If it is known that the (population) standard deviation of such expenditures is $20, and if the total expenditures for the 50 families interviewed was $11,600, construct a 95% confidence interval for the mean monthly expenditures for families of four.
2. Suppose X1 and X2 are a random sample of size 2 from a normal population with variance 2,500. Find the probability that X1 and X2 are within 50 of each other.
3. A random sample of 100 accounts of persons having Royal Credit cards was taken and the mean balance due was found to be $110.72. If the standard deviation of all balances is $46, find a 95% confidence interval for the mean balance due for all Royal credit card holders.

Computer Exercise:

Do either problem 1 or problem 2:

1. The dataset which we collected in our class contains the following variables:

• year = student's class
• female = 1 if female =0 if male
• height = student's height
• cig = number of cigarettes smoked per day
• hair = cost of last haircut
• gpa = student's GPA
• gpa = student's roommate's GPA
• exc = hours a week spent exercising
• tv = hours a week spent watching TV
• stud = hours a week spent studying
• stud253 = hours a week spent studying for econ 253

1. Download the data classdata.txt or classdata.xls or classdata.dta and load it into stataquest.
2. Calculate sample mean of hours spent studying and its sample standard deviation.
3. What is the 95% confidence interval for hours studying?
4. Test the hypothesis that Williams students study fewer than 15 hours a week.

2. The dataset indexes.txt contains 6 variables:
   • date = July 1954 - December 2000
   • SP500 = S&P500 price index closings
   • DJI = Dow Jones Industrial Average price index closings
   • cpi = Consumer Price Index 1982-84=100 from Bureau of Labor Statistics
   • tbill = interest rate on 3 month treasury bill
   • ffr = federal funds rate
   Do the following exercises:
   1. Download the file indexes.txt or indexes.xls or indexes.dta and load it into stataquest.
   2. Create a new variable for percentage monthly returns on the S&P500 index.
   3. Calculate the sample mean and the sample standard deviation of monthly returns
   4. What is the probability that the population mean of S&P500 returns is negative?
   5. What is the 95% confidence interval for the monthly returns?