Quantitative Methods for Business
You have been hired as an intern by the Colonial Daily Crier, a small newspaper in the Bay Area in Northern
California. The Crier collects a lot of data about its business and wants to improve its decision making by
using the data effectively. Your role as a bright and shiny analyst is to use the data available to help
management think about their business and address a number of specific questions they want answered.
Managing the Colonial Daily Crier
The Colonial Daily Crier is a daily newspaper that has been published continuously since the late 1950s.
The Crier serves the Bay Area with a circulation of approximately 170,000 on weekdays and 250,000 on
During the past decade, the Crier has acquired and consolidated a number of small competing publications
and has claimed the leadership position in advertising lines and revenues. In 2001, the Crier established
an internet presence with the Crier OL (on-line) edition. Like any well-run business, the management of
the Crier seeks to continue to grow its media business by increasing revenues and lowering expenses
through increased effectiveness and efficiency.
The production manager at the Crier has initiated some quality improvement efforts. The first project
relates to the blackness of the newspaper printing. The production manager measures the blackness of
the print using a standard scale where the target value is 2.0. A blackness measure that is less than 1.75
or greater than 2.25 is not conforming to specifications. Each day, they have measured blackness on one
spot of the first newspaper printed. Data from the past year shows that the blackness is approximately
normally distributed, with a mean of 2.1 and a standard deviation of .20. The goal is to improve printing
performance and manage the production system toward consistently meeting the target.
Advertising income is a critical source of revenue for the Crier, as it is for any media outlet. The Crier
hopes to increase revenues and reduce costs in the advertising area. To this end, the Crier wants to
analyze the performance of the advertising customer service group and find out what if any improvements
can be made. They have reviewed the advertising process and collected a great deal of data about
advertising errors as well as calls to the advertising help desk (Table 1 & Table 2; spreadsheet
‘advertising’). In addition to categorizing and quantifying the types of advertising errors, the data also
indicates the root cause of the error.
Table 1: Advertising Data
Table 2: Help Desk Call Data
In addition to the revenue generated by advertising, newspaper delivery subscriptions generate revenue
for the Crier, as well as provide a forecast of how many papers are needed on a daily basis. Subscriptions
are sold when a customer calls the Crier to purchase a subscription, or via telemarketing sales. The Crier
only conducts telemarketing calls on weekdays during the evening hours between 5 PM and 9 PM. In the
industry, yields on telemarketing are notoriously low, there is high employee turnover, and telemarketers
are paid only on the number of sales they generate. At the Crier, telemarketers are paid by the hour, not
by the sale. Telemarketers are trained by the Crier to adhere to a structure for each call, utilizing a script
to guide the conversation and sales presentation.
In order to assess the effectiveness of the telemarketing process, a sample of 15 telemarketers were
selected on a randomly chosen evening. Each telemarketer was observed twice during the work shift,
Type of Error # of Errors
Total Cost of
Copy error 108 326
Layout 14 30
Omits 26 365
Pasteup 22 215
Poor reproduction 16 130
Ran in error 60 1082
Rate quote 26 53
Space not ordered 14 129
Typesetting 106 531
Velox 56 233
Wrong ad 50 536
Wrong date 28 359
Wrong position 90 1314
Wrong manual pasteup 25 165
Wrong size 12 53
Day Calls Day Calls Day Calls Day Calls Day Calls Day Calls
1 45 16 18 31 34 46 70 61 60 76 46
2 30 17 41 32 75 47 75 62 54 77 31
3 53 18 63 33 88 48 42 63 35 78 26
4 69 19 72 34 63 49 23 64 46 79 60
5 67 20 44 35 38 50 38 65 51 80 59
6 45 21 45 36 48 51 11 66 58 81 83
7 17 22 44 37 42 52 71 67 72 82 71
8 46 23 40 38 50 53 80 68 86 83 49
9 46 24 48 39 74 54 70 69 48 84 51
10 33 25 67 40 61 55 41 70 57 85 50
11 59 26 72 41 28 56 47 71 51 86 56
12 74 27 39 42 37 57 33 72 62 87 49
13 42 28 52 43 27 58 38 73 62 88 94
14 35 29 45 44 44 59 29 74 70 89 73
15 38 30 40 45 49 60 83 75 76 90 42
once between 5 – 7 PM, and once between 7 – 9 PM. The telemarketers were aware that a study was
being conducted, but did not know the date of the study or the specific telemarketers who were being
observed. Data from the study is available in Table 3 (spreadsheet ‘telemarketing’).
Table 3: Telemarketing Data
New subscriptions are often sold as trial subscriptions, with a discount provided for the first 3 months.
The goal of the Crier in offering this trial subscription is to get people ‘hooked’ on home delivery, and
hopefully convert them to regular subscribers. The Crier has been using a subjective process based on
the most recent three months of data to forecast the number of new subscriptions, but has found that
this subjective approach is increasingly inaccurate. The marketing department feels that the hours of
telemarketing calls could be used to forecast the number of new subscriptions each month. Luckily, the
telemarketing team has maintained careful records for the hours of telemarketing completed each month
(Table 4; spreadsheet ‘historical telemarketing data’).
Call Duration (measured in seconds)
Telemarketer Early Late Seniority
Charlie 41.3 39.5 Senior
Meghan 37.5 38.9 Junior
Jack 39.3 42.2 Junior
Ann 39.5 45.7 Senior
Renee 33.6 42.4 Junior
Katie 38.5 42.1 Senior
Richard 32.6 43.5 Senior
Jen 37.3 40.5 Junior
Jane 40.6 40.7 Junior
Hugh 33.3 38.0 Senior
Susan D. 39.6 43.6 Junior
Chris 35.7 43.8 Senior
Susan H. 31.3 34.9 Junior
Steve 36.8 35.7 Junior
Chase 36.3 47.4 Junior
Table 4: Monthly Telemarketing Data: Hours Worked and New Subscriptions
The telemarketing industry standard is to compensate telemarketers strictly on a per sale basis, without
any hourly pay as a base pay. The Crier has always paid its telemarketers on an hourly basis, which means
that employees with low sales yields receive the same pay as those who generate high sales volumes. The
marketing department has been testing a modified hybrid pay system, where telemarketers are paid both
a base, hourly rate and an additional incentive for sales. The marketers are very excited about this new
system. There is speculation that this incentive system will increase motivation in the telemarketing force,
as well as increase sales of new subscriptions. Over the last 24 weeks, the marketing department has
conducted a beta test to examine the effect of the new incentive program and the number of hours of
telemarketing on new subscriptions. Two levels of incentives have been adopted by the new
compensation system: telemarketers received either a modest (incentive = low), or a rather generous
lump sum (incentive = high). The data for this period has been collected and appears in Table 5
(spreadsheet “compensation changes”).
Table 5: Weekly Trial Data - Compensation Changes
Subscriptions Hours Compensation
1 1884 282 High
2 2108 336 High
3 1655 232 High
4 2000 321 Low
5 1463 261 Low
6 1154 212 High
7 878 162 High
8 1385 266 Low
9 1677 269 High
10 851 185 Low
11 1212 191 High
12 1508 226 High
13 2049 331 Low
14 1770 311 Low
15 1277 222 High
16 1272 227 Low
17 1550 257 High
18 999 193 High
19 1934 325 High
20 1260 216 Low
21 1493 251 High
22 2156 345 Low
23 1700 286 Low
24 1842 263 High
The management team of the Crier is committed to using quantitative tools and analytical techniques in
order to understand its business better. They are looking for you to identify the quantitative tool to use,
perform the analysis, interpret the results, and formulate recommendations based on that analysis. They
have identified a number of areas for you to focus on, identified below. Use the case and spreadsheets
provided to address their questions, and report your answers to 2 decimals as appropriate.
1 Think about the Crier’s production process. (14 points)
A Based on data from the past year, what is the probability that the blackness of the spot is more than
2.0? Between 1.75 and 2.25?
B Working toward the goal of increasing conformance to specifications, should the production manager
focus on moving the mean closer to 2.0 or reducing the standard deviation to .1? Why?
2 Think about the Crier’s advertising customer service group, focusing on the data available about
advertising errors and help desk calls. (14 points)
A What are the most important issues to address in order to reduce both the number of and the cost
associated with errors? What specific area should be investigated further? Explain your reasoning and
include one or two graphs to support your analysis.
B How would you describe the volume of help calls to the Crier? What do you think the shape of this
sample is? Write a sentence (or two) that is detailed and specific.
3 The Crier management team believes that the longer a telemarketer talks to a potential customer,
the more likely it is that they will sell a new subscription. (20 points)
A Based on the data, test the hypothesis that there is a difference in call duration if calls are placed
early in the evening versus late in the evening. Describe in detail the statistical test you are using,
show your analysis/output, and interpret the findings of your test (=.05). Write a sentence or two
to communicate your findings.
B Based on the data, test whether senior telemarketers, on average, have longer calls than the average
overall call duration. Describe in detail the statistical test you are using, show your analysis/output,
and interpret the findings of your test (=.05). Write a sentence or two to communicate your
C The Crier believes that longer calls have a higher probability to result in new subscriptions and is
going to hire additional telemarketers. In order to increase yield and based on your results in parts A
and B, what recommendations would you make to the Crier about who they should hire and what
schedule the new people should work?
D What reservations or assumptions are made in using the telemarketing data for the above analysis?
4 The Crier wants to use the data it has available to improve its new subscription forecasting technique.
A Develop a regression model to predict the number of new subscriptions for a month, based on the
hours invested in telemarketing. Show your analysis/output. Describe the model in terms of the line
formula. Interpret the values of the coefficients.
B Is the model statistically significant at the .05 level of significance? At the .01 level of significance?
How strong is the model? Write a sentence or two describing the level of significance and the specific
strength of the model.
C If the Crier expects to have 1,300 hours of telemarketing in a given month, what is your estimate of
the average number of new subscriptions for the month. What about 2,000 hours of telemarketing?
D Is there any evidence that the data is not appropriate for use in regression. Explain your conclusion
5 The Crier wants to understand the effect of the new compensation system. (26 points)
A Develop a regression model to forecast new subscriptions considering the number of telemarketing
hours and the type of compensation system used. Show your analysis/output. Describe the model in
terms of the line formula. Interpret the values of the coefficients. Is the model statistically significant
at the 0.05 level of significance? How strong is the model?
B Compare the two regression models (from Q4A and Q5A) developed to forecast new subscriptions.
Which is a better model? How can you tell? Explain your conclusion.
C Is there evidence that there is an interaction effect between the type of compensation and the
number of telemarketing hours? Explain your conclusion based on the model.
These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.
1 A Based on data from the past year, what is the probability that the blackness of the spot is more than 2.0? Between 1.75 and 2.25?
Based on data from the past year, the probability for the blackness of the spot to be more than 2.0 is 69.15%. Based on the same data, there is 73.33% probability for the blackness of the spot to be between 1.75 and 2.25.
B Working toward the goal of increasing conformance to specifications, should the production manager focus on moving the mean closer to 2.0 or reducing the standard deviation to .1? Why?
If the production manager is trying to increase conformance to specifications, he should reduce the standard deviation to 0.1 as it has 93.29% probability that the blackness of the spot would be between 1.75 and 2.25. If he moves the mean closer to 2.0, there would only be 78.88% probability that the blackness of the spot would be between 1.75 and 2.25.
2. A What are the most important issues to address in order to reduce both the number of and the cost associated with errors? What specific area should be investigated further? Explain your reasoning and include one or two graphs to support your analysis.
In order to bring down the number of erros and the cost associated with errors, it is important that Crier analyzes its cost per error. If it analyzes the number of errors and the total cost of errors, it may help with its income but the cost per error will be an even more accurate field in order to increase revenues and reduce costs. It is noteworthy that while...