MGSC2301 PROJECT #3 (Conf Int/Hypo Test) complete solutions correct answers key

MGSC2301 PROJECT #3 (Conf Int/Hypo Test) complete solutions correct answers key

This project again utilizes the data set for the Bank and Trust Company (B&T); the random sample of 222 employees and data recorded for several variables:

·     Annual salary earned by the employee; 

·     The age of the employee;

·     The years of experience in the banking industry held by the employee prior to

        joining B&T;

·     The education level of the employee;

·     The extent to which the employee uses a computer;

·     The grade classification within B&T held by the employee;

·     The years of experience at B&T;

·     The gender of the employee;

·     The citizenship of the employee; and

·     A location adjustor for salary using a 1-5 scale.

Assume that you still work for Ms. Deanna V. Ashun (aka “Dee”) and that the lawsuit alleging gender bias has been resolved in favor of B&T.  But more work remains, and Ms. Ashun has asked you to complete several tabulations and calculations, excluding the CEO from all calculations.

 Note: Assume normality!!!

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

#1:  (a)      What is the point estimate for the average annual salary paid to B&T

                  employees in each of the six grades?

                  Please round your answers to the nearest whole dollar.

                  (12 points)

       (b)      For the Vice Presidents (GRADE 6) only, find the 95% Confidence Interval

                  for the average annual salary.

                  (2 points)

       (c)       Ms. Ashun’s boss, Mr. Samuel Pellsize, is an intelligent man, but has

                  limited statistical training.  In a maximum of two sentences, provide a

                  managerial interpretation of your numeric result from part (1b); this

                  interpretation will be read by Mr. Pellsize.

                  (2 points)

       (d)      For part (b), did you use the Finite Population Correction Factor? 

                  Why or why not? (4 points)

Mr. Pellsize is glad that the gender bias lawsuit has been resolved, but does still wonder about B&T’s promotion practices.  For example, he is aware that in the sample being used, 14 out of 15 vice presidents are male.   Since many of the vice presidents are promoted from within, this leads to a concern that B&T might not have an adequate pool of female senior officers (GRADE 5).  So he wonders if B&T exhibits some form of gender bias in terms of the promotion of branch managers/junior officers (GRADE 4) to senior officers (GRADE 5). 

Note:  this is often referred to a glass ceiling for women.

Mr. Pellsize and Ms. Ashun decide to be pro-active and start an investigation.

#2:  Ms. Ashun quickly asks you for the following calculations:

(a)   What proportion of the branch managers/junior officers (GRADE 4) is female?

       (2 points)

(b)   What proportion of the senior officers (GRADE 5) is female?

       (2 points)

(c)   Find a 99% confidence interval for the proportion of females in GRADE 4.

       (2 points)

(d)   Find a 95% confidence interval for the proportion of females in GRADE 5.

       (2 points)

(e)        Assuming your reader is Mr. Pellsize, explain the numerical values found in part

       (2c &            2d) above – using a maximum of two sentences.

       (2 points)

Still somewhat concerned, Ms. Ashun asks you to continue to focus on the B&T employees in GRADES 4 and 5.  She does some research – investigating other North American banks the size of B&T.  She finds that on average, branch managers in other banks get paid an average of 80,000/year and that senior officers get paid an average of $90,000/year.  She wonders if B&T pays comparable salaries.

#3:  (a)      Find the average salary for the females in GRADE 4.

                  Please round your answer to the nearest whole dollar.

                  (2 points)

       (b)      If:       mFemales4 = average salary for all B&T females in GRADE 4

Test the following hypothesis using a =0.01(Assume normality):

                                       H0:      mFemales4  £ $80,000

                  vs                  Ha:      mFemales4 > $80,000

                  Specify if you reject or fail to reject H0.

In the context of the problem specify your final conclusion in words.

                  (3 points)

       (c)       Find the average salary for the males in GRADE 4.

                  Please round your answer to the nearest whole dollar.

                  (2 points)

       (d)      If:       mMales4 = average salary for all B&T males in GRADE 4

Test the following hypothesis using a =0.01 (Assume normality):

                                       H0:      mMales4  £ $80,000

                  vs                  Ha:      mMales4 > $80,000

                  Specify if you reject or fail to reject H0.

In the context of the problem specify your final conclusion in words.

                  (3 points)

       (e)       Find the average salary for the females in GRADE 5.

                  Please round your answer to the nearest whole dollar.

                  (2 points)

       (f)       If:       mFemales5 = average salary for all B&T females in GRADE 5

Test the following hypothesis using a =0.05 (Assume normality):

                                       H0:      mfemales5  £ $90,000

                  vs                  Ha:      mfemales5 > $90,000

                  Specify if you reject or fail to reject H0.

In the context of the problem specify your final conclusion in words.

                  (3 points)

       (g)      Find the average salary for the males in GRADE 5.

                  Please round your answer to the nearest whole dollar.

                  (2 points)

       (h)      If:       mMales5 = average salary for all B&T males in GRADE 5

Test the following hypothesis using a =0.05 (Assume normality):

                                       H0:      mMales5  £ $90,000

                  vs                  Ha:      mMales5 > $90,000

                  Specify if you reject or fail to reject H0.

In the context of the problem specify your final conclusion in words.

                  (3 points)

NAME(S):                         _____________________________________

                                          _____________________________________

                                          _____________________________________

           SCORE (out of 50):                    ______________________

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

#1:  (a)      Point estimates for average annual salary by grade, rounded to nearest whole dollar:

Grade of B&T Employee

         Estimated Annual Salary

                      1

            $

                      2

            $

                      3

            $

                      4

            $

                      5

            $

                      6

            $

       (b)      95% C.I. for average annual

                  salary of GRADE 6 Employees =  [  $ _____________  ,  $ ______________  ]

(c)       Managerial interpretation of (1b):  (to be read by Mr. Pellsize)

                  _____________________________________________________________

                  ____________________________________________________________

                  _____________________________________________________________

       (d)      Finite Population Correction Factor was used?     ¯        YES        ¯           NO           

                  Rationale:     ______________________________________________

                                       ______________________________________________

                                       ______________________________________________

#2:  (a)      pFEMALE in GRADE 4 = ____________________________

       (b)      pFEMALE in GRADE 5 = ____________________________

       (c)       99% C.I. for pFEMALE in GRADE 4  =   (  _______________ , _______________ )

       (d)      95% C.I. for pFEMALE in GRADE 5  =   (  _______________ , _______________

       (e)       Explanation of 99% C. I. for pFEMALE in GRADE 4:

                  ____________________________________________________________

                  ____________________________________________________________

                  Explanation of 95% C. I. for pFEMALE in GRADE 5:___________________

                                                                                                          _

#3:  (a)      Average annual salary for females in GRADE 4:            XFemales4 = ____________

       (b)      Hypothesis test (a = 0.01):                     H0:      mFemales4  £ $80,000

                                                                       vs       Ha:      mFemales4 > $80,000

                  Conclusion:             ð  Fail to reject H0                    ð      Reject H0

                  Conclusion in context of problem:

ð       I/we are 99% confident that on average, female branch

managers at B&T earn annual salaries in excess of $80,000.

ð     There is no enough evidence to conclude that female branch managers at B&T earn average annual salaries in excess of $80,000.

ð             I/we are 99% confident that on average, female branch managers

at B&T earn annual salaries of $80,000 or less.

                                                                                                          _

       (c)       Average annual salary for males in GRADE 4:    XMales4 = ____________

       (d)      Hypothesis test (a = 0.01):                     H0:      mMales4  £ $80,000

                                                                       vs       Ha:      mMales4 > $80,000

                  Conclusion:             ð  Fail to reject H0                    ð      Reject H0

                  Conclusion in context of problem:

ð       I/we are 99% confident that on average, male branch                             managers at B&T earn annual salaries in excess of $80,000.

ð       There is no enough evidence to conclude that male branch

managers at B&T earn average annual salaries in excess of $80,000.

ð       I/we are 99% confident that on average, male branch

managers at B&T earn annual salaries of $80,000 or less.

                                                                                                          _

       (e)       Average annual salary for females in GRADE 5:            XFemales5 = ____________

       (f)       Hypothesis test (a = 0.05):                     H0:      mFemales5  £ $90,000

                                                                       vs       Ha:      mFemales5 > $90,000

                  Conclusion:             ð  Fail to reject H0                    ð      Reject H0

                  Conclusion in context of problem:

ð       I/we are 95% confident that on average, female senior

officers at B&T earn annual salaries in excess of $90,000.

ð       There is no enough evidence to conclude that female senior officers

at B&T earn average annual salaries in excess of $90,000.

ð     I/we are 95% confident that on average, female senior officers at B&T earn annual salaries of $90,000 or less.

                                                                                                          _

       (g)      Average annual salary for males in GRADE 5:    XMales5 = ____________

       (h)      Hypothesis test (a = 0.05):                     H0:      mMales5  £ $90,000

                                                                       vs       Ha:      mMales5 > $90,000

                  Conclusion:             ð  Fail to reject H0                    ð      Reject H0

                  Conclusion in context of problem:

ð       I/we are 95% confident that on average, male senior

officers at B&T earn annual salaries in excess of $90,000.

ð       There is no enough evidence to conclude that male senior

officers at B&T earn average annual salaries in excess of $90,000.

ð       I/we are 95% confident that on average, male senior

officers at B&T earn annual salaries of $90,000 or less.