Name:                      

                                                                                           FINAL EXAM

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.  In many universities, students evaluate their professors by means of answering a questionnaire.  Assume a questionnaire is distributed to a class of 15 students.  Students are asked to answer the following questions:

  • How much did you learn in this course?

Exceptional amount _____                 A lot ______        Very little _____

  • Age ____
  • Class Standing (Fr, So, Jr, Sr)
  • Grade Point Average _____
  • The textbook is very effective

1

2

3

4

5

Strongly Agree

Moderately Agree

Neutral

Moderately Disagree

Strongly Disagree

a.  How many elements are in the above data set?  (3 points)

 

 

b.  How many variables are in this data set? (3 points)

 

 

c.  Which variables are qualitative and which are quantitative?  How can you tell? (5 points)

 

 

 

 

 

2.  Distinguish between descriptive statistics and statistical inference.  Use an example to show how the two concepts differ.  (16 points)

 

 

 

 

 

 

 

 

 

 

3.  The age of 16 employees are shown below.  Use this data to develop a frequency and relative frequency distribution.  Use statistical inference to make two comments on employee age for this firm.  (15 points)

22

40

34

36

35

27

30

32

39

46

32

48

45

36

41

41

4.  The per-pound prices of two goods, chocolate cupcakes and spaghetti, are shown below for each month in 1986.

 

 

Cupcake

Spaghetti

Jan

$2.235

$0.741

Feb

2.218

0.74

Mar

2.253

0.748

Apr

2.239

0.743

May

2.284

0.734

Jun

2.285

0.748

Jul

2.327

0.731

Aug

2.299

0.737

Sep

2.37

0.732

Oct

2.402

0.727

Nov

2.272

0.729

Dec

2.356

0.747

 

a.   Determine the mean and median price of both cupcakes and spaghetti in the year.  Fully explain the meaning of each. (10 points)

 

 

 

 

 

 

b.  Determine the standard deviation of both goods for the year.  Fully explain their meaning. (10 points)

 

 

 

 

 

 

 

c.  If the price of cupcakes and spaghetti were distributed normally, at what prices (specifically) would you consider “outliers” for each good?  Explain your reasoning. (6 points)

 

 

 

 

 

 

 

 

d The sample covariance between these goods is -.00018.  Interpret this value.  Calculate the sample correlation coefficient between these goods.  Interpret this value.  (9 points)

 

 

 

 

 

 

6.  As a contractor, you have submitted a bid to build two apartment buildings.  You estimate that the probability of winning the first contract is .67, the probability of winning the second contract is .20, and the probability of winning both contracts is .33.  

a.  You believe that the success of two bids are independent.  Explain the meaning of this assumption.  (6 points)

 

 

 

 

 

 

 

b.  What is the probability that you will win at least one of the bids?  (4 points)

 

 

 

c.  Assume that you are told that you have successfully won the bid for the first project.  Now that you know this information, what is the probability that you will be successful on the second bid?  (4 points)

 

 

 

 

7.  Your grandma loves to buy scratch-off lottery tickets at the convenience store.  The state says that 3% of the tickets are winners in the sense that the purchaser of the ticket will receive a prize.  Grandma buys you 15 tickets for Christmas. 

a.  What is the probability that you will win exactly one time?  (4 points)

 

 

 

b.  What is the probability that you will win at least twice?  (5 points)

 

 

 

 

 

 

8.  The scheduling manager for a certain hydropower utility company knows that there is an average of 12 emergency calls regarding power failures per month.  Assume that a month consists of 30 days.

a.  Find the probability that the company will receive exactly 10 emergency calls during a specified month.  (5 points)

 

 

 

 

 

b.  Suppose the utility company can handle a maximum of 3 emergency calls per day.  What is the probability that there will be more emergency calls than the company can handle on a given day?  (6 points)

 

9.  When calculating probabilities, explain the difference between discrete probability distributions (like the binomial) and continuous probability distributions (like the normal).  (10 points)

 

 

 

 

 

 

 

 

 

 

10.  A statistics professor notes that the grades of his students were normally distributed with a population mean of 80.04 and a population standard deviation of 6.13.  The professor has informed us that 6.3% of his students received A’s while only 2.5% of his students failed the course and received F’s.

a.  What is the minimum score needed to make an A?  (4 points)

 

 

 

 

b.  What is the maximum score among those who received an F?  (4 points)

 

 



11.  A department store has determined that 18% of their customers are from out of state.  A random sample of 36 sales is selected.

a.  Describe the defining characteristics of this sampling distribution of the sample proportion.  (6 points)

 

 

 

 

 

 

b.  What is the probability that the sample proportion will be between .14 to .30?  (5 points)

 

 

 

 

 

 

 

 

 

 

 

 

12.  Interested in changing academic standards, you randomly sample students from the current senior class and the current freshman class.  You then calculate point estimators in the table below.  Have incoming ACT scores significantly changed?  Carefully set up and conduct the hypothesis test and then explain your results to the Dean of Admissions.  (12 points)

Class of 2008

Class of 2005

Sample size = 24

Sample size = 17

Sample mean ACT = 25.21

Sample mean ACT = 27

Sample standard deviation ACT = 3.134

Sample standard deviation ACT = 4.757

 

 

 

 

 

 

 

 

 

 

 

 

13.  The percentage of students who enroll at a college or university, and actually graduate, is an important statistic for university administrators.  Some of the factors related to the graduation rate include the percentage of classes with fewer than 20 students, the percentage of classes with more than 50 students, the student-faculty ratio, the percentage of students who apply to the university and are admitted (how selective the university is), the percentage of first-year students in the top 10% of their high school class, and the academic reputation of the university.  Data for 48 national universities was collected.

  • Graduation rate is your dependent variable.
  • % of Classes Under 20:  the percentage of classes with fewer than 20 students.
  • % of Classes of 50 or more: the percentage of classes with more than 50 students.
  • Student-Faculty Ratio:  The ratio of the number of students enrolled divided by the total number of faculty.
  • Acceptance Rate:  The percentage of students who apply and are accepted.
  • 1st-Year Students in Top:  The percentage of students admitted who were in the top 10% of their high school class.
  • Academic Reputation Score:  A measure of the school’s reputation determined by surveying administrators at other universities.  Measured on a scale from 1 (marginal) to 5 (distinguished)

 

In your analysis, please clearly separate your responses into these parts.

a. Interpret each of the estimated coefficients.  Do they make economic sense?  Explain.  (14 points)

b. Discuss how well the model fits the data.  (6 points)

c. Discuss statistical significance, being sure to explain the appropriate hypothesis tests. (16 points)

d. What is multicollinearity?  In this model of graduation rates, do you see the potential for this problem?  How would you check for it and how might you adjust your model accordingly?  (4 points)
NOTE:  You may need to complete some missing information. (11 points)

SUMMARY OUTPUT

 

 

 

 

 

Regression Statistics

 

 

 

 

Multiple R

0.874554829

 

 

 

 

R Square

 

 

 

 

 

Adjusted R Square

 

 

 

 

 

Standard Error

4.468824563

 

 

 

 

Observations

48

 

 

 

 

 

 

 

 

 

 

ANOVA

 

 

 

 

 

 

df

SS

MS

F

Significance F

Regression

6

 

443.8550924

22.2256564

1.88742E-11

Residual

41

818.786112

19.97039298

 

 

Total

47

3481.916667

 

 

 

 

 

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

 

Intercept

 

 

11.67611487

7.271947665

6.82689E-09

 

% of Classes Under 20

 

-0.169549258

0.096720653

-1.752978838

 

 

% of Classes of 50 or More

 

 

0.19611488

-2.571395942

0.013853439

 

Student/Faculty Ratio

 

-0.264338381

0.260773307

 

 

 

Acceptance Rate

 

 

0.055833427

-3.738399257

0.000566225

 

1st-Year Students in Top 10% of HS Class

0.129942773

0.058095898

2.236694448

 

 

Academic Reputation Score

 

1.92178851

2.048466604

0.046953102