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 35 12 13 11 5 3 2 2

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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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
2
3
4
5
6
7
8
35
9
10
11 or more than 11
22H54 22 NO
12
13
11
Number of complaints received when not being served by a Virtual Agent Observed Frequency
0
1
3
2
0
19
14
15
HONGINN NO
9
14
6
4
2
2
3
2
(b) Test the hypothesis that the average number of complaints received per day when
served by a Virtual agent is the same as the number of complaints received per
day after not being served by a Virtual Agent at the 5% significance level.
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 2 3 4 5 6 7 8 35 9 10 11 or more than 11 22H54 22 NO 12 13 11 Number of complaints received when not being served by a Virtual Agent Observed Frequency 0 1 3 2 0 19 14 15 HONGINN NO 9 14 6 4 2 2 3 2 (b) Test the hypothesis that the average number of complaints received per day when served by a Virtual agent is the same as the number of complaints received per day after not being served by a Virtual Agent at the 5% significance level.
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