Use only the space provided to answer the following questions.  Whenever possible, show your work for potential partial credit.  You may use the extra sheets of paper for additional space.  NOTE:  When performing numerical calculations, keep at least 4 decimals.  (i.e., do NOT round .2265 to .227 or .23)

1.  You are tired of hearing that the Dean of Admissions at Hanover College has been successful at significantly increasing the average SAT scores of incoming first year students, but you are skeptical.  You randomly sampled students from the current senior class of 2005 and the current freshman class of 2008.  You then calculated point estimators in the table below.  Have incoming SAT scores significantly increased?  Carefully set up and conduct the hypothesis test and then explain your results to the Dean of Admissions.  (10 points)

Class of 2008

Class of 2005

Sample size = 22

Sample size = 6

Sample mean SAT = 1140.455

Sample mean SAT = 1111.667

Sample standard deviation = 99.4019

Sample standard deviation = 135.5606

 

 

 

 

 

 

 

 

 

 

2.  You are considering a change in production techniques in an attempt to decrease the length of time that it takes your employees to complete a task.  Faster completion of the task will save the firm money.  You select six workers and have each complete the production task with the old method and then complete the task with the new method.  The table below summarizes the task completion times for the matched sample.  Is the new method faster?  First describe, and then conduct a hypothesis test to come to a conclusion.  (16 points)

Worker

Completion Time for

Old Method (minutes)

Completion Time for

New Method (minutes)

1

6

5.4

2

5

5.2

3

7

6.5

4

6.2

5.9

5

6

6

6

6.4

5.8

 

3.  The topic of your Independent Study is drug experimentation by college students and you have asked students whether they have ever tried illegal drugs and whether or not they are currently in a dating relationship.  You are testing the hypothesis that the proportion of students that have experimented with illegal drugs differs between students who are, and who are not, in a dating relationship.  The relevant data is in the table below.  Be sure to clearly state the hypothesis, confidence level of the test, and test statistic.  Clearly explain the results of your test to someone unfamiliar with such testing techniques.  (15 points)

Students in a

Dating Relationship

Students not in a

Dating Relationship

Sample size = 54

Sample size = 38

Sample proportion who have tried

illegal drugs = .4815

Sample proportion who have tried

illegal drugs = .5806

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4.  A 10-year study conducted by the American Heart Association provided data on how age, blood pressure, and smoking relate to the risk of strokes.  The dependent variable is “Risk” and measures the probability that the patient will have a stroke over the next 10 year period.  The independent variables are:

Age:  The age (in years) of a patient.

Pressure:  The blood pressure of a patient.

Smoke:  A dummy variable equal to 1 if the patient is a smoker and 0 if they are not a smoker.

a.  For each of these independent variables, prior to conducting least-squares regression, do you expect a positive or negative sign on each?  Why?  (6 points)

 

SUMMARY OUTPUT

 

 

 

 

 

 

 

 

 

 

 

Regression Statistics

 

 

 

 

Multiple R

0.934605168

 

 

 

 

R Square

 

 

 

 

 

Adjusted R Square

 

 

 

 

 

Standard Error

5.756574565

 

 

 

 

Observations

20

 

 

 

 

 

 

 

 

 

 

ANOVA

 

 

 

 

 

 

df

SS

MS

F

Significance F

Regression

3

3660.739588

1220.246529

36.82301223

2.06E-07

Residual

16

530.2104116

33.13815073

 

 

Total

19

4190.95

 

 

 

 

 

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

 

Intercept

-91.75949844

 

-6.027783261

1.75755E-05

 

Age

1.076741057

0.165963611

 

 

 

Pressure

 

0.045225519

5.567951023

 

 

Smoker

 

3.000815432

2.912498704

0.010173553

 

b.         Begin by computing and filling-in any necessary omitted information.  (8 points)

 

c.         Now that you have some Excel output, carefully interpret each estimated coefficient.  Does the sign of each slope coefficient make economic sense?  How? (8 points)

 

 

 

 

 

 

 

 

 

 

d.  What do your results tell you with regards to the statistical significance of each coefficient?  Be thorough and include the necessary hypothesis test(s).  (12 points)

 

 

 

 

 

 

 

 

 

 

 

e.  Interpret and use the appropriate measure(s) to comment upon the ability of the estimated model to fit the data.  (8 points)

 

 

 

 

 

 

 

 

f.  What can you say about overall significance for this model?  What does this mean?  Again, be thorough and include the necessary hypothesis test(s).  (6 points)

 

 

 

 

 

 

 

 

 

 

g. What is muticollinearity?  In this model of stroke risk, do you see the potential for this problem?  How would you check for it and how might you adjust your model accordingly?  (11 points)