BUSN 5760 Applied Business Statistics

Final Exam

 

Dr. Elizabeth Hair

Summer 2009

 

  1. Use the following to answer questions:  The table below presents the probability distribution for X = the number of email messages you will receive in the next 10 minutes. (9 pts)

 

 

X

0

1

2

3

P(X)

.35

.35

.25

.05

 

 

a.    What is the probability that no emails will be received?

 

b.    What is the probability that at least one email will be received?

 

c.    What is E(X), the expected number of emails that will be received?

 

d.    What is Var(X), the variance of the number of emails that will be received?

 

e.    What is the Std(X), the standard deviation of the number of emails that will be received?

 

  1. Site preparation for new housing developments for tracts of 50 houses are normally distributed with a mean of 200 and a standard deviation of 10 workdays.  (9 points) 

 

a.    Find the probability that the site is completed within 185 workdays

 

b.    Find the probability that the site will not be completed within 215 workdays

 

c.    Find the probability that the site is completed between 185 and 215 days. 

 

  1. What is the difference between a statistic and a parameter? (6 points)

 

  1. Describe Type I and Type II error (6 points)

 

 

 

  1. John Rengel is the Quality Assurance Supervisor for Vino Supremo Vinyards.  He knows that 10 percent of each box of corks is undersized. (10 pts)   

a)    If he were to randomly select 120 corks from the next box, then how many of these corks would John expect to be undersized?

b)    If he were to randomly select 120 corks from each box, then what would John calculate as the standard error of the number of undersized corks?

c)    What is the probability that John will find 15 or more corks defective in a randomly selected box?

  

  1. Sixto Sanchez is the owner of Suburban Stylists.  He is evaluating the service level provided to walk-in customers. Because he is enrolled in an MBA program at Eastern University, Sixto decides to sample walk-in customers for the next two weeks.  He collects information from 82 walk-in customers and calculates that their average waiting times that is 21 minutes with a standard deviation of 4 minutes.  (10 pts)  

a)         Determine the degrees of freedom to be used in further analysis.

b)         Calculate the two sided 95% confidence interval for the population mean of waiting times.

c)         Calculate the two sided 90% confidence interval for the population mean of waiting times.

d)         Calculate the two sided 99% confidence interval for the population mean of waiting times.

e)         What t table value should be used in calculating a two sided 95% confidence interval for the population mean of waiting times if the sample selected is 25 instead of 82?

  

 


 
  1. Bay Area Community College (BACC) has collected data comparing the starting salaries of their graduating students with last names beginning with the letters A through M with those whose last names begin with N through Z.  The first category provided 47 random responses with an average starting salary of $29,426.42 and a standard deviation of $4,521.94.  The second category had 52 random responses with an average starting salary of $22,863.81 and a standard deviation of $2,378.66. (10 pts) 

 

a)    If you assume that last names should not have an impact on starting salary of graduates of BACC, then what is the appropriate null hypothesis?

b)    State the research hypothesis in words and in notation.

c)    Calculate the appropriate test statistic.

d)    Calculate the appropriate p-value for the test statistic.

e)    Is the statistic statistically significant?

f)     What type of error if any has been committed?

 

  1. Plymouth Rock Securities is interested in finding out if there is a relationship between the number of new clients brought into the firm by a broker and the sales performance of the broker. A random sample of 11 brokers' records are reviewed to determine the number of new clients enrolled last year and total sales in millions of dollars:  (10 pts)

 

Broker

1

2

3

4

5

6

7

8

9

10

11

Clients

27

11

42

33

15

15

25

36

28

30

17

Sales, $

52

37

64

55

29

34

58

59

44

48

31

 

a)    How closely related is the new client base to sales performance?  Draw the scatterplot and compute the correlation and describe the relationship

b)    Find the least-squares equation to predict sales from number of clients. Can the least squares equation be used to predict sales?

c)    What does the slope represent?

d)    What would a new broker who brings in 30 clients sell, on average?

e)    How much of the variability in sales is not explained by the number of new clients?

 


 
  1. Jean Siskel is an entertainment analyst for West Coast Securities. He is trying to develop a model to estimate gross earning generated by a new movie release.  He has collected the following data on 20 movies: Gross Earnings, Production Costs, Promotion Costs, and if the movie is based on a bestseller novel: (10 pts)

 

 

Gross Earnings

Production Cost

Promotion Cost

 

Movie

Millions $

Millions $

Millions $

Novel

1

28

4.2

1

0

2

35

6

3

1

3

50

5.5

6

1

4

20

3.3

1

0

5

75

12.5

11

1

6

60

9.6

8

1

7

15

2.5

0.5

0

8

72

10

12

1

9

45

6.4

8

1

10

37

7.5

5

0

11

30

5.0

1

1

12

63

10.1

10

0

13

58

7.8

9

1

14

50

6.9

10

0

15

24

3.5

4

0

16

82

11.0

15

1

17

48

10.7

1

1

18

34

6.6

2

0

19

50

8.4

3

1

20

45

10.8

5

0

  

a.           What type of variable is novel?

b.           What is the estimated multiple linear regression equation derived from this data?

c.           What are the regression coefficients for each X variable?  Interpret the regression coefficient.

d.           Will Jean be pleased with the results?

e.           Interpret the intercept value.

 


 

 

  1. The following data represent revenues in thousands of dollars for a manufacturer of small electric appliances. (10 pts)

 

Year

Quarter

Revenues

1996

1

  514

1996

2

  822

1996

3

  648

1996

4

  976

1997

1

  616

1997

2

  884

1997

3

  678

1997

4

  996

1998

1

  658

1998

2

  850

1998

3

  714

1998

4

1052

 

 

a)         Calculate the moving averages for this time series.

b)         Find the seasonal index for each quarter.

c)         From the fourth quarter of 1997 to the first quarter of 1998, revenues declined.  What happened on a seasonally adjusted basis?

d)         Compute the forecast for the second quarter of 2002.

extra credit (+2)     Find the regression equation to predict the long term trend in the seasonally adjusted revenues.

 


 
  1. Bay Area University enrolls MBA students in three cohort programs: Weeknight, Saturday, and Distance. Dean Ed Epstein wants to know if there is a difference in the average of the students in the three programs.  He has his assistant take a random sample of 5 students from each program and record their ages. (10 pts)

 

Weeknight

Saturday

Distance

29

32

25

27

33

24

30

31

24

27

34

25

28

30

26

 

a)         State the Null hypothesis and the Research hypothesis to be tested

b)         Calculate the grand average.

c)         Calculate the between-sample variability.

d)         Calculate the within-sample variability.

e)         Calculate the F statistic.

f)          Should the Null hypothesis be rejected at the 5% level of significance?

g)         Draw box plots for the different programs.

h)         Using the least-significant difference test, identify the significant differences between the programs.

 

EXTRA CREDIT:  Please describe the different parts of a statistical report and what is included in each section.  (5pts)