NAME:                                  

You may use additional sheets of paper to solve the following questions, but please report your results and conclusions in the space provided.  Whenever possible, show your work for potential partial credit.  NOTE:  When performing numerical calculations, keep at least 4 digits after a decimal.  (I.e., do NOT round .2265 to .23 or .227)  BUDGET YOUR TIME WISELY!

1.  As a favor to the Dean of Admissions, you are going to perform some statistical analysis, including a hypothesis test that will test the research question:  “Does the average Hanover College student experience a lower GPA in college than they did in high school?”  Describe, in great detail, the step-by-step methodology that you would use to set up, perform, and conclude this test.  I am not interested in specific calculations, do not make up data or an outcome, just tell the story from beginning to end.  (20 points)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.  Like most fall semesters, I am currently teaching two sections of Principles of Microeconomics, and, although they receive the same assignments and exams, I am concerned about whether the performance differs between the two sections.  The table below summarizes the mean class grade, as a proportion of the total possible points, and the number of students in each section.  Set up, conduct, and explain the results of a hypothesis test to help me address my concerns.  (12 points)

Section A

Section B

n = 18 students

n = 16 students

Mean grade = .7987

Mean grade = .7956

 


3.  As a consultant to the airline industry, you are given an assignment to develop a simple linear regression model between the number of customer complaints (per 100,000 passengers) and the percentage of flights that arrive on time.

a.  Write the theoretical simple linear regression equation for this model, being sure to specify which variable should be the dependent variable.  Explain why you chose this variable as the dependent variable.  What is the expected sign of the slope coefficient?  Explain your reasoning.  (8 points)

 

 

 

 

 

 

b.  Least squares estimation will produce the intercept and slope of the estimated regression line.  In addition to these estimates, what other pieces of information would you find useful in completing your assignment?  What does this information tell you and why is it useful?  (10 points)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4.  In order to determine whether or not there is a difference between the hourly wages of two companies, the following data have been accumulated.

Company 1

Company 2

Sample size = 80

Sample size = 60

Sample mean wage = $6.75

Sample mean wage = $6.25

Sample standard deviation = $1.00

Sample standard deviation = $0.95

Your nosy roommate comments that, since one wage is higher than the other that the problem ends there.  Explain to your roommate why it is not as simple as that.  Then conduct an appropriate test to determine whether there is any significant difference between the hourly wages of the two companies.  Explain the results to your roommate.  (15 points)


5.  Supermarkets frequently price products such as bread and milk to attract customers to the store.  A manager of a dairy that supplies milk to a supermarket wanted to know how sales of milk are affected by different prices.  Consequently, she recorded the weekly sales (Sales) of milk at one supermarket, the price of a quart of her company’s brand (Own Price) and the price of a quart of her competitor’s brand (Rival Price).

a.  Prior to conducting least-squares regression, which of these three economic variables should be the dependent variable?  Do you expect a positive or negative sign on each independent variable?  In responding to these questions, be sure to use economic analysis to explain your reasoning.  (9 points)

 

 

 

 

 

 

 

 

 

Using Excel, you produce the following table of information.  Use this output to answer the questions below.  Sales are measured in number of quarts sold per week.  Milk prices are measured in cents per quart.

SUMMARY OUTPUT

 

 

 

 

 

 

 

 

 

Regression Statistics

 

 

 

Multiple R

0.702328063

 

 

 

R Square

 

 

 

 

Adjusted R Square

0.472581635

 

 

 

Standard Error

558.6819057

 

 

 

Observations

52

 

 

 

 

 

 

 

 

ANOVA

 

 

 

 

 

df

SS

MS

F

Regression

2

14887582.57

7443791.287

23.84871

Residual

49

15294148.12

312125.4718

 

Total

51

 

 

 

 

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Intercept

 

857.5655311

4.336660978

7.19E-05

Own Price

-46.7736569

10.83136113

 

7.64E-05

Rival Price

58.52364212

10.46412923

 

9.86E-07

b.  Begin by computing and filling in any necessary omitted information.  (5 points)

 

c.  Carefully interpret each estimated coefficient.  Do they make economic sense?  Explain.  (6 points)

 

 

 

 

 


d.  What do the results tell you with regards to the statistical significance of each coefficient?  Be thorough and include the necessary hypothesis tests.  (9 points)

 

 

 

 

 

 

 

 

 

 

 

 

 

e.  Interpret and use the appropriate measure to comment upon the ability of the estimated model to fit the data.  (6 points)