Business Statistics: Analysis of Customer Service Errors, Call Data, Cost of Errors, and Probability Distribution

This article provides an analysis of customer service errors, call data, cost of errors, and probability distribution using business statistics. It also discusses ethical dilemmas and adherence to ethical guidelines.

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BUSINESS STATISTICS
PART 1
Chapter 2
Question 1
The respective bar chart for the type of customer service errors is highlighted below.
The errors with a relative frequency in excess of 5% would be considered as significant.
From the above graph, the following errors are significant.
 Incorrect accessory
 Incorrect address
 Incorrect contact phone
 Website access errors
 Wrong billing
 Wrong start date
 Wrong subscription
The additional information pertaining to the above errors would be related to the underlying
reason for these errors. For instance, the reason behind incorrect details could be an error on
the end of the consumer, an error on the end of the representative or a systemic error. This
needs to be probed further so that the fix can address the issue. One potential solution for the
company would be to automate processes especially bill generation along with customer
details. Further, the various contact details should be verified before entering into the system.

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Also, key information for each account should also be verified so as to improve the customer
service.
Question 2
The descriptive statistics related to the calls made data is presented below.
It is apparent that on an average about 52 calls were made to the helpdesk on a daily basis.
Also, o on 50% days, calls received were at most 49. However, there seems to be a
significant variation considering the wide range whereby the lowest calls received varies
from 11 to 83. Also, there is presence of positive skew which implies that on certain days, the
amount of calls received is exceptionally high which is reflective of the poor services
provided by the company. Ideally, the skew should be expected to be negative which would
auger well for the quality of services (Flick, 2015).
Chapter 3
Question 1
The most critical variable is the cost associated with the various errors. The descriptive
statistics with regards to the same are indicated below.

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The requisite boxplot is indicated below.
0
20
40
60
80
100
120
140
Question 2
The graphical display of the cost associated with the various errors is as shown below.

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Incorrect accessory
Incorrect address
Incorrect contact phone
Invalid wiring
On-demand programming errors
Subscription not ordered
Suspension error
Termination error
Website access errors
Wrong billing
Wrong end date
Wrong number of connections
Wrong price quoted
Wrong start date
Wrong subscription type
0
20
40
60
80
100
120
140
Cost of errors
Type of errors
Cost ($ 000's)
The boxplot does not provide information about the breakup of the costs in terms of the
errors. However, this information can be obtained from the above graph where it is apparent
that top three contributors to cost are wrong billing, incorrect address and wrong subscription
type. Hence, the graph above allows the organisation to compare the costs and thereby list
down the key priorities (Hair et. al., 2015).
Question 3
Based on the descriptive statistics computed for cost, it is apparent the mean cost due to a
particular error is $ 46,750. Also, the dispersion with regards to the costs seems medium to
high considering the range and standard deviation. Also, the cost data has a positive skew
implying that some of the costs are quite high and rather unexpected. Further, the given cost
is not normally distributed owing to presence of skew due to which the graph would be
asymmetric (Eriksson & Kovalainen, 2015). Also, the above observations are also supported
from the boxplot which also indicates presence of an outlier on the higher side in the form of
wrong billing cost. Further, the graphical display highlights that top three contributors to cost
are wrong billing, incorrect address and wrong subscription type.
Chapter 5

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Question 1
The given probabilities can be computed using a binomial distribution with the following
parameters.
Number of trials (n) = 50
Probability of success (p) = 0.02 (since no free premium channels are used)
a) Less than 3 customers should subscribe
Hence, requisite probability = P(0) + P(1) + P(2)
Using excel function BINOMDIST, P(0) = 0.3642, P(1) = 0.3716, P(2) = 0.1858
Hence, probability = 0.3642 + 0.3716 + 0.1858 = 0.9216
b) Requisite probability = P(0) + P(1) = 0.3642 + 0.3716 = 0.7358
c) Requisite probability = 1- (P(0) + P(1) + P(2) + P(3) +P(4)) = 1-
BINOMDIST(4,50,0,02,true) = 1- 0.9968 = 0.0032
d) Actual probability = 4/50 = 0.08
It is apparent that the previous estimate for subscription is wrong considering that the
actual probability based on the given data is four times the estimated probability of 0.02.
Question 2
The given probabilities can be computed using a binomial distribution with the following
parameters.
Number of trials (n) = 50
Probability of success (p) = 0.06 (since two free premium channels are used)
a) Less than 3 customers should subscribe
Hence, requisite probability = P(0) + P(1) + P(2)

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Using excel function, P(0) = 0.0453, P(1) = 0.1447, P(2) = 0.2262
Hence, probability = 0.0453 + 0.1447 + 0.2262 = 0.4162
b) Requisite probability = P(0) + P(1) = 0.0453 + 0.1447 = 0.19
c) Requisite probability = 1- (P(0) + P(1) + P(2) + P(3) +P(4)) = 1-
BINOMDIST(4,50,0.06,true) = 1-0.8206 = 0.1794
d) It is apparent for all the three cases i.e.(a) to (c), the answers obtained are lesser as
compared to the previous question as the estimated probability of subscription is higher on
account of two free channels being given. As a result, the probability values for the
distribution are more widely distributed in this case.
e) Actual probability = 6/50 = 0.12
It is apparent that the previous estimate for subscription is wrong considering that the
actual probability based on the given data is twice the estimated probability of 0.06.
Chapter 9
Question 1
The sample data constituting of 50 observations of upload speeds has been presented as
indicated below.
The sample mean (computed using excel) = 0.95872
The testing of the hypothesis can be carried out as shown below.
Null Hypothesis: μ ≥ 0.97

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Alternate Hypothesis: μ < 0.97
Since the population standard deviation is not available, hence the appropriate test statistics
would be t and a left tail t test would be conducted.
Sample mean = 0.95872
Sample standard deviation = 0.156
Sample size = 50
Hence computed value of t statistic = (0.95872-0.97)/(0.156/500.5) = -0.5114
The p value associated with the above test statistics would exceed 0.05(assumed significance
level) and hence the available evidence is not sufficient to reject the null hypothesis (Eriksson
& Kovalainen, 2015).
Question 2
Date: April 1, 2018
On the basis of the available sample data, it can be concluded that the technical department
has been successful in ensuring that all the internet subscribers have a mean upload speed of
atleast 0.97. This augers well for the company and the services provided. However, the
company should aim to reduce the standard deviation in the upload speed which is available
to various subscribers or else there may be certain customers who might not be happy on
account of slower upload speed than claimed (Flick, 2015).

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PART 2
It is apparent that in the given case there is an ethical dilemma since my leader expects me to
use business statistics to produce results that would support that speeds would increase if the
new equipment would be bought. However, acting under the pressure of my superior would
undermine my commitment to the employer and also the shareholders of the organisation
whose interest I should uphold at all times through my conduct. Further, entertaining this
request would amount of fraud and my personal values of being truthful and faithful are in
clear contradiction with the instructions I have received (Swartz, 2017).
The ethical guideline adhered by me for this situation would be to remain faithful to my
employer. As a result, I would not engage in any activity which adversely impacts the
shareholders. The fact that the given situation involves statistics and ethics further supports
my stance as the statistical analysis usually provides reliable results, thereby leaving limited
scope for altering the conclusion. Thereby, complying with the orders of my seniors could
potentially have disastrous consequences for me in the future if it found that the equipment
does not improve speed.
According to the Christian Worldview, mankind has fallen and prone to sin. However, we are
accountable for our actions. Hence, by being deceitful, I do not want to commit any sin. It is
imperative to set an example not only for myself but for others also that one should not
engage in unethical actions with the purpose of fulfilling material desires. Essentially, we
should focus on Jesus for redemption since there is no other mechanism that we can redeem
ourselves from the sins that we have committed. Hence, further sinful actions would not
achieve anything but further me from redeeming myself through God (Slick, 2008). Thus, in
this situation I would not comply with the order my supervisor has given me and would not
falsify the results.

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References
Eriksson, P. & Kovalainen, A. (2015) Quantitative methods in business research (3rd ed.).
London: Sage Publications.
Flick, U. (2015) Introducing research methodology: A beginner's guide to doing a research
project (4th ed.). New York: Sage Publications.
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., & Page, M. J. (2015) Essentials of
business research methods (2nd ed.). New York: Routledge.
Slick, M. (2008) What are some Christian Worldview Essentials? Retrieved from
https://carm.org/what-are-some-christian-worldview-essentials
Swartz, M. (2017) Business Ethics: An Ethical Decision-Making Approach (2nd ed.) London:
Wiley & Sons