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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)