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Mathematics & Economics

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Statistics Project

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# Conf Int/Hypo Test: The Bank And Trust Company (Statistics Project Sample)

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Follow all question and answer questions, thanks.

source..Content:

Project #2 (Conf Int/Hypo Test)
Your Name
Your Institution of Affiliation
March 30, 2018
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)
Point estimate Mean$70671
(b) For the Vice Presidents (GRADE 6) only, find the 95% Confidence Interval
for the average annual salary.
(2 points)
Confidence Interval Estimate for the MeanDataSample Standard Deviation48044.42681Sample Mean70671.17117Sample Size222Confidence Level95%Intermediate CalculationsStandard Error of the Mean3224.530798Degrees of Freedom221t Value1.9708Interval Half Width6354.7641 Confidence IntervalInterval Lower Limit64316.41Interval Upper Limit77025.94
(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)
We are 95% confident that the average salary is lies between the $64316 and $77026.
(d) For part (b), did you use the Finite Population Correction Factor?
Why or why not? (4 points)
We don’t use the finite population correction factor because there is adequate sample size given.
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)
Required proportion = 0.39
(b) What proportion of the senior officers (GRADE 5) is female?
(2 points)
Required proportion = 0.21
(c) Find a 99% confidence interval for the proportion of females in GRADE 4.
(2 points)
Confidence Interval Estimate for the ProportionData Sample Size222Number of Successes86Confidence Level99%Intermediate CalculationsSample Proportion0.387387387Z Value-2.5758Standard Error of the Proportion0.0327Interval Half Width0.0842 Confidence IntervalInterval Lower Limit0.3032Interval Upper Limit0.4716
(d) Find a 95% confidence inte...

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