Quantitative Fluency

Case Study #1
Flight Delays
As an advisor to the small regional airport, you have been asked
to look into the relationship between the delay times for flights
and the length of the flight overall (measured in miles). The local
division of the Federal Aviation Administration (FAA) has
supplied you with a simple random sample of 20 recent flight
delays for your analysis. The division would also like to know if
the average flight delay times for this year are higher or lower
than last year’s average flight delay time of 42 minutes.
Length of flight (nearest 5
miles)
Flight Delay (in
minutes)
720 5
1,090 16
400 3
920 11
800 6
900 6
1,400 23
1,150 12
190 1
240 2
950 8
850 10
960 11
320 2
290 3
820 7
555 7
1,005 9
950 9
540 4
Quantitative Fluency, Level B Summative Assessment: Outline & Rubric
Case Study #2
Brand Name Change
A company has recently changed its brand name and would like
to determine the effect (if any) on customers’ perceived
satisfaction with its products.
The company has provided you with a random sample of 20
products and their average customer satisfaction rating before
and after the brand name change. Customer ratings range from
0 to 10 (10 representing the highest rating possible).
Determine whether there is a difference in customer satisfaction
ratings before and after the brand name change.
Product
Customer
Satisfaction
Rating (before)
Customer
Satisfaction
Rating (after)
Headset A 2.4 2.7
Speakers 8.9 7.6
CD Player 5 6
DVD Player 7.2 7.1
Alarm Clock 9 8.4
Stereo 8.8 8.6
Shower Radio 7.7 7.7
Surround System 6.1 6.0
Satellite Radio 6.3 5.9
Microphone 4.3 8.2
Bluetooth Speakers 1.1 3.4
Karaoke System 2.6 3.5
Earbuds 7.2 7.5
Gaming Headset 8 8.9
Expanding Speaker 5.1 6.2
Portable Speaker 7.9 7.6
Multimedia Speaker 5.6 5.7
Phone Charger 5.2 5.3
Wireless headphones 6.4 7.8
Portable Keyboard 8.2 8.1
Quantitative Fluency, Level B Summative Assessment: Outline & Rubric
Case Study #3
Insurance Claims
Veracity Insurance Company is analyzing its current policy rates. When the
company first determined their rates, it was expecting an average claim
amount of $1,500. After a few years, it has reason to believe that the true
claim amount is higher than this figure and would like to determine a more
profitable policy rate. Veracity selects 21 random claim amounts to analyze.
Determine whether Veracity should change its current policy rates.
Claim Amounts
Claimant ID Claim Amount
JD43129 $820
SM55763 $999
EA12985 $1,010
RS28563 $2,078
QX55732 $3,900
YT65987 $3,045
YD23791 $1,800
PL34345 $1,950
HS21900 $1,962
LS88654 $900
OK45342 $560
DV77654 $432
LK67501 $4,010
RD54873 $5,060
PY98712 $105
LO90765 $6,010
AH76432 $1,822
HP90776 $1,756
EA76235 $2,300
JM66543 $2,001
HC89785 $2,180
Quantitative Fluency, Level B Summative Assessment: Outline & Rubric
Case Study #4
Salaries (by gender)
It is claimed that women make 75 cents to every dollar a man makes
when they work the same job. An organization decides to test this
claim by collecting a random sample of reported salaries for 21 job
titles.
Determine whether there is a significant difference in the average
salaries for men and women for this particular organization.
Job Title
Salary
(Male)
Salary
(Female)
Accountant $82,000 $79,000
Auditor $76,000 $76,200
Budget Analyst $92,000 $89,900
Business Operations Specialist $65,000 $62,000
Claims Adjustor $79,400 $71,500
Tax Preparer $42,000 $35,000
Personal Financial Advisor $110,000 $109,000
Human Resource Specialist $56,000 $62,100
Investment Banker $248,000 $252,000
Loan Counselor $25,000 $27,000
Credit Analysts $73,000 $76,500
Professional Development
Officers $79,900 $61,400
Insurance Appraisers $52,700 $49,800
Management Analyst $88,000 $89,000
Purchasing Agents $56,000 $51,000
Cost Estimators $52,450 $53,350
Training and Development
Specialists $49,870 $49,700
Insurance Underwriters $92,000 $67,500
Emergency Management
Specialists $47,800 $49,200
Clerical Assistant $27,100 $29,000
Customer Service Representative $30,500 $28,300
Quantitative Fluency, Level B Summative Assessment: Outline & Rubric
Case Study #5
Correlation
The managers of NorthSpire, a manufacturing company based in
Washington, have asked your consulting firm to analyze whether
worker productivity levels are affected by length of employment. They
collect records, from a random sample of 20 employees, of the
duration of each employee’s tenure with NorthSpire and his/her
associated productivity level.
Productivity level is measured by the percentage of target output (of
manufactured units) met, recorded monthly and averaged over the
entire year (e.g., a productivity level of 80% indicates that on average,
the employee has met 80% of the monthly targets for that year).
Duration of
Employment
(years)
Annual
Productivity
Level
(Percentage of
target output per
month)
5 115%
7 100%
2 98%
1 101%
12 105%
21 105%
2 95%
5 96%
6 92%
1 89%
11 82%
10 101%
7 98%
15 106%
4 99%
4 102%
9 110%
1 94%
2 105%
15 90%