MSC 300 Marymount Some Nonparametric Statistics Case Study Analysis

CHAPTER 7 HYPOTHESIS TESTING CASE STUDYHypothesis testing can be important when developing performance standards for your subordinates.
Each of you will be a manager, and each of you will therefore need to develop performance
standards which will clearly allow you (and your subordinate) to agree as to whether or not the
subordinate met your requirement. You do not want to end a rating period with disagreement on
the subordinate’s performance, and you do not want to lose a grievance to upper management
should the subordinate appeal your performance rating. (A subordinate certainly has every right to
appeal, but you should never lose an appeal!)
Suppose that you are manager of a restaurant, and need to develop a series of performance
standards for each member of your staff. The restaurant is a full-service restaurant, with seated
customers, menus, a hostess to meet customers and seat customers, etc. Examples might include
Joe Theismann’s, an IHOP, an Outback Steakhouse, etc.
For this case study, develop one measurable, numeric performance standard for a member of the
wait staff. Then show how you could take a random sample of 30 readings of the performance and
develop a hypothesis test using the t statistical method to determine, at 95% confidence, if the
performance standard was met. List 30 notional (hypothetical) “readings” and calculate a
corresponding notional t-test to show how your subordinate hypothetically performed. You will
need to calculate the sample mean, sample standard deviation, use the t table in the back of the
book, etc., to complete the analytics. You must use Excel to log your data and perform many or all
of your analytics, and you will submit your Excel file (and any other files you may find convenient to
submit such as photos of your calculations if done long-hand). This may be a one-tail test.
At the 95% confidence level, using the notional data, can you conclude that the subordinate is
meeting your standard.
CASE STUDIES: CHAPTER 7 HYPOTHESIS TESTING CASE STUDY
GRADING RUBRIC
Student name:
a. State the null hypothesis. 1 pt.
b. State the alternative hypothesis. 1 pt.
c. State the significance level. 1 pt.
d. Perform the calculations. 3 pts.
e. What is your conclusion. Discuss why or why not you would statistically accept the null
hypothesis, with the understanding that you could be wrong 5% of the time. Also discuss if this is a
total fair test of if other circumstances need to be considered before drawing any final conclusions –
the numbers do not always tell the entire story. 3 pts.
CHAPTER 8 SOME NONPARAMETRIC STATISTICS CASE STUDY AND
GRADING RUBRIC
Student Name.
A person has just taken a new job, and is experimenting with two approaches to getting to work.
Taking the Metro for ten days, she experiences the travel times below. For the next 10 days, she
“slugs” by hitching a ride with other commuters from the local gas station. Her commute times
in minutes are recorded below, also. Based on the data below, if she wants to take the travel
method having the shortest duration, — should she take Metro, “slug,” or are they both about the
same duration. Use the 95% confidence level.
Metro
45
36
39
51
72
31
30
34
37
38
Slug
60
25
28
34
58
33
32
35
36
29
a. State the null hypothesis. 1pt.
b. State the alternative hypothesis. 1 pt.
c. State the significance level. 1.pt.
d. Perform the calculations. Include the median travel times for each travel method. You may use
Excel. 3 pts.
e. Draw the conclusions. 3 pts.
2. You work for the US federal government and were selected to build a new small organization
within your Agency. There has been a federal regulation change, and your office will be needed to
perform the corresponding analytics necessary to measure your Agency’s compliance with the new
regulation. Your organization will also be tasked to perform a variety of other analytics assignments.
You will be hiring people already working for your Agency in some other capacity to fill the newly
created job positions.
This is going to be an Analytics organization of 20 people, so you have developed the job
descriptions needed and given them to HR. HR sends out the new jobs announcements within the
Agency, and screens applicants so that only those qualified (i.e., those who meet your job description
requirements) are passed on to you for your selection. You convene a small committee of senior
analytics people to review the applications passed on by HR and make the final selections.
A recent internal hiring action by another group in the Agency resulted in selection with bias
towards gender, and the selection process had to be redone. The Agency is therefore currently very
sensitive to gender bias. It is very important to internally fill the new positions without bias towards
gender – only qualifications are to be considered. You need to produce a sound argument to your
supervisor (and by extension, the Agency), that gender was not a factor in the selection. Below is a
table of those applicants who made it through the HR qualification selection process, and those your
committee selected for the new positions. Statistically, is there an indication that demographic
group was a factor in the selection process. Assume that HR passed along all applications to you
without demographic bias in their selection process.
Gender
# Applications received from HR (qualified for the new positions)
# Applicants selected for the new positions
a. State the null hypothesis. 1 pt.
b. State the alternative hypothesis. 1 pt.
c. State the significance level. 1 pt.
d. Perform the calculations. 3 pts.
A
32
15
B
12
5
e. What is your conclusion. Discuss why or why not you would statistically accept the null
hypothesis, with the understanding that you could be wrong 5% of the time. Also reflect on the fact
that three times as many gender A were selected than gender B. 3 pts.
e. What is your conclusion. Discuss why or why not you would statistically accept the null
hypothesis, with the understanding that you could be wrong 5% of the time. Also discuss if this is a
total fair test of if other circumstances need to be considered before drawing any final conclusions –
as the numbers do not always tell the entire story. 3 pts.
CHAPTER 8 SOME NONPARAMETRIC STATISTICS CASE STUDY AND
GRADING RUBRIC
Student Name.
A person has just taken a new job, and is experimenting with two approaches to getting to work.
Taking the Metro for ten days, she experiences the travel times below. For the next 10 days, she
“slugs” by hitching a ride with other commuters from the local gas station. Her commute times
in minutes are recorded below, also. Based on the data below, if she wants to take the travel
method having the shortest duration, — should she take Metro, “slug,” or are they both about the
same duration. Use the 95% confidence level.
Metro
45
36
39
51
72
31
30
34
37
38
Slug
60
25
28
34
58
33
32
35
36
29
a. State the null hypothesis. 1pt.
b.
Both the Metro and “slug” means are the same duration
b. State the alternative hypothesis. 1 pt.
Metro is takes shorter or longer duration than “slug”,
c. State the significance level. 1. Pt.
Significance level is 0.05
d. Perform the calculations. Include the median travel times for each travel method. You may use
Excel. 3 pts.
T-value Calculation
s2p = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22) = ((9/18) * 155.57) + ((9/18) * 146) = 150.78
s2M1 = s2p/N1 = 150.78/10 = 15.08
s2M2 = s2p/N2 = 150.78/10 = 15.08
t = (M1 – M2)/√(s2M1 + s2M2) = 4.3/√30.16 = 0.78
e. Draw the conclusions. 3 pts.
At p