A family software company operating in 4 cities in the UK would like to automate customer service and reduce repeat calls in their call centres. Hence, they would like to fully implement Al-powered virtual agents in order to reduce costs as well as enhance the customer service performance. In order to fully understand consumer acceptance of this new technology, they collected data from a pilot survey during the last 90 days on the number of complaints received after contacting customer service and being served either by a virtual agent or not (e.g. served by a human agent or directed to the FAQS (Frequently Asked Questions) online page, among others). The relevant data are presented in the following tables below: Number of complaints received when being served by a Virtual Agent Observed Frequency 0 1 2 3 5 7 3 5 35 12 13 10 11 or more than 11 11 5 4 10 11 or more than 11 Number of complaints received when not being served by a Virtual Agent Observed Frequency 3 2 19 14 15 9 14 2 2 3 2 0 (e) Find an approximation to the 95% confidence interval for the difference of the average number of complaints received in the two types of customer service (with or without Virtual Agent).

A First Course in Probability (10th Edition)
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A family software company operating in 4 cities in the
UK would like to automate customer service and reduce repeat calls in their call
centres. Hence, they would like to fully implement AI-powered virtual agents in order
to reduce costs as well as enhance the customer service performance. In order to fully
understand consumer acceptance of this new technology, they collected data from a
pilot survey during the last 90 days on the number of complaints received after
contacting customer service and being served either by a virtual agent or not (e.g.
served by a human agent or directed to the FAQS (Frequently Asked Questions) online
page, among others). The relevant data are presented in the following tables below:
Number of complaints received when being served by a Virtual Agent Observed Frequency
0
1
2
3
4
5
6
7
8
9
10
11 or more than 11
C200 100 100 9
1
3
4
Number of complaints received when not being served by a Virtual Agent Observed Frequency
5
6
7
8
9
10
35
12
13
11 or more than 11
222 22-
11
3
0
19
14
15
9
14
6
ONENNDO
2
2
3
2
0
(e) Find an approximation to the 95% confidence interval for the difference of the
average number of complaints received in the two types of customer service (with
or without Virtual Agent).
Transcribed Image Text:A family software company operating in 4 cities in the UK would like to automate customer service and reduce repeat calls in their call centres. Hence, they would like to fully implement AI-powered virtual agents in order to reduce costs as well as enhance the customer service performance. In order to fully understand consumer acceptance of this new technology, they collected data from a pilot survey during the last 90 days on the number of complaints received after contacting customer service and being served either by a virtual agent or not (e.g. served by a human agent or directed to the FAQS (Frequently Asked Questions) online page, among others). The relevant data are presented in the following tables below: Number of complaints received when being served by a Virtual Agent Observed Frequency 0 1 2 3 4 5 6 7 8 9 10 11 or more than 11 C200 100 100 9 1 3 4 Number of complaints received when not being served by a Virtual Agent Observed Frequency 5 6 7 8 9 10 35 12 13 11 or more than 11 222 22- 11 3 0 19 14 15 9 14 6 ONENNDO 2 2 3 2 0 (e) Find an approximation to the 95% confidence interval for the difference of the average number of complaints received in the two types of customer service (with or without Virtual Agent).
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