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 (i.e. step 1, step 2, etc) 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.  A sample of 1545 men and a sample of 1681 women were used to compare the amount of housework done by women and men in dual-earner marriages.  The study showed that 67.5% of the men felt the division of housework was fair and 60.8% of the women felt the division of housework was fair (American Journal of Sociology, September 1994).  Is the proportion of men who felt the division of housework was fair greater than the proportion of women who felt the division of housework was fair?  Support your conclusion with a statistical test using a .05 level of significance.  (12 points)

 

3.  As a consultant to the automobile industry, you are given an assignment to develop a simple linear regression model between the number of automobiles sold per year and per-capita income in the U.S. 

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.  (6 points)

 

 

 

 

 

b.  What is the expected sign of the slope coefficient?  Explain your reasoning.  (6 points)

 

 

 

 

 

 

c.  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.  More and more people are using the Internet to book airline tickets.  It is important for consumers that websites are fast and efficient in their ability to give the web surfer the necessary flight information.  In order to determine whether or not there is a difference between the time that it takes to find flight information on the websites of two airlines, the following data have been accumulated.

Delta

Northwest

Sample size = 22

Sample size = 20

Sample mean time = 2.5 minutes

Sample mean time = 2.1 minutes

Sample standard deviation = .8 minutes

Sample standard deviation = 1.1 minutes

Your nosy roommate comments that, since one time is faster 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 time that it takes to find flight information on these two corporate websites.  Explain the results to your roommate.  (15 points)

5.  Heller Company manufactures lawn mowers and related lawn equipment.  The managers believe the quantity of lawn mowers sold depends on the price of the mower and the price of a competitor’s mower.  Let

y= quantity sold (1000s)

x1 = price of competitor’s mower ($)

x2 = price of Heller’s mower($)

a.  Prior to conducting least-squares regression, do you expect a positive or negative sign on each independent variable?  .  In responding to these questions, be sure to provide economic analysis to explain your reasoning.  (6 points)

 

 

 

 

 

 

Using Excel, you produce the following table of information.  Use this output to answer the questions below. 

SUMMARY OUTPUT

 

 

 

 

 

 

 

 

 

 

 

Regression Statistics

 

 

 

 

Multiple R

0.807917582

 

 

 

 

R Square

 

 

 

 

 

Adjusted R Square

0.553511054

 

 

 

 

Standard Error

18.73618138

 

 

 

 

Observations

10

 

 

 

 

 

 

 

 

 

 

ANOVA

 

 

 

 

 

 

df

SS

MS

F

Significance F

Regression

2

4618.788552

2309.394

6.578637

0.024679244

Residual

7

2457.311448

351.0445

 

 

Total

9

 

 

 

 

 

 

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Intercept

 

41.87708331

1.5884

0.156219

-32.50592763

Competitor's
Price

0.413915255

 

1.589608

0.155948

-0.201804615

Heller's
Price

 

0.080905005

-3.33454

0.012513

-0.461090502

 

b.  Begin by computing and filling in any necessary omitted information.  (4 points)

 

c.  Carefully interpret each estimated coefficient.   (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)