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.             A recent Time magazine reported the following information about workers in Germany and the United States:                                                                                US                           Germany

                Average length of workweek (hours)                                 42                              38

                Standard Deviation                                                                  5                                6

                Sample Size                                                                           600                            700

At 95% confidence, test to determine whether or not there is a significant difference between the average workweek in the United States and the average workweek in Germany.  Thoroughly explain the results of the test, including the original hypothesis.  (15 points)

 

 

 

 

 

 

 

 

 

 

 

2.             A school administrator believes that there is no difference in the student dropout rate for schools located in his district and schools located in another district, and she has asked for your help.  A random sample of 25 schools in the administrator's district was taken.  The student dropout rate of the schools in the sample was 24%.  A random sample of 30 schools in the other district had a dropout rate of 27%.

                a.     Give a point estimate for the difference between the population proportions for the two districts.  (2 points)

 

 

                b.     State the null and alternative hypotheses.  (4 points)

 

 

 

                c.     Test the hypothesis stated in Part b at the 1% significance level.  (6 points)

               

 

 

 

 

 

                d.     For the school administrator, explain what you have done.  What do you conclude?  If you choose a 5% significance level, would your conclusion change?  Why?  (10 points)

 

3.  To determine the effectiveness of a new weight control diet, 5 randomly selected students observed the diet for 4 weeks with the results shown below.  (Consider these to be matched samples, with the difference (d) = Before – After.)

Use the data below to test the hypothesis that the new diet will help you lose weight.  State the null hypothesis, show your work, and explain your results.  Should this diet be promoted as effective?  Why?  (15 points)

 

                                            Dieter              Weight Before                     Weight After

                                                  A                           138                                          135

                                                  B                           151                                          147

                                                  C                           129                                          132

                                                  D                           125                                          127

                                                  E                            168                                          155

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CASE 1:  Alumni donations are an important source of revenue for colleges and universities.  If administrators could determine the factors that could lead to increases in the percentage of alumni who make a donation, they might be able to implement policies that could lead to increased revenues.  Research shows that students who are more satisfied with their contact with teachers are more likely to graduate.  As a result, one might suspect that smaller class sizes and lower student-faculty ratios might lead to a higher percentage of alumni who make a donation.  Data for 48 colleges and universities has been collected and the following variables are defined as:

Ø       % Under 20:  the percentage of classes with fewer than 20 students enrolled.

Ø       Student/Faculty Ratio:  the number of students enrolled divided by the number of faculty employed.

Ø       Alumni Giving Rate:  the percentage of all alumni who made a donation to the university (dependent variable).

Ø       Graduation Rate:  the percentage of students who initially enrolled at the university and graduated.

a.             For each of these independent variables, justify their inclusion into a model where the dependent variable is Alumni Giving Rate.  In other words, prior to conducting least-squares regression, do you expect a positive or negative sign on each?  Why?  (6 points)

 

 

 

 

 

 

 

 

Using Excel, you get the following regression output.  Use this output to answer the questions below.

SUMMARY OUTPUT

 

 

 

 

 

Regression Statistics

 

 

 

 

Multiple R

0.836624531

 

 

 

 

R Square

 

 

 

 

 

Adjusted R Square

0.679482011

 

 

 

 

Standard Error

7.609724781

 

 

 

 

Observations

48

 

 

 

 

ANOVA

 

 

 

 

 

 

df

SS

MS

F

Significance F

Regression

3

 

1981.177024

34.21254509

1.43233E-11

Residual

44

2547.948094

57.90791124

 

 

Total

47

8491.479167

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

 

Intercept

 

17.52136501

-1.182563933

0.243333057

 

 Graduation Rate

0.748182799

 

4.508212716

4.799E-05

 

% Under 20

0.029040648

0.139321322

 

0.835844489

 

Student/Faculty Ratio

-1.192010694

0.386723104

-3.082336383

0.003538403

 

 

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

 

c.             Now that you have some Excel output, carefully interpret each estimated coefficient.  Does the sign of each 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.  (6 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).  (5 points)

 

 

 

 

 

 

 

 

 

g.             What is multicollinearity?  Would you suspect multicollinearity in this model?  Where is it most likely to exist?  What kinds of statistical information would you need to determine whether or not multicollinearity is present?  (6 points)