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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 35 12 13 11 5 4 3 2 2 2 1 0 Number of complaints received when not being served by a Virtual Agent Observed Frequency 0 1 2 3 4 5 6 7 8 9 10 11 or more than 11 19 14 15 9 14 6 4 2 2 3 2 0 (a) Estimate the average number of complaints received per day in the two different types of customer service where a customer is served by a Virtual Agent or not served by a Virtual Agent. Test the hypothesis that the average number of complaints received per day when served by a Virtual agent is the same the number of complaints received per day after not being served by a Virtual Agent at the 5% significance level (c) 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 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 35 12 13 11 5 4 3 2 2 2 1 0 Number of complaints received when not being served by a Virtual Agent Observed Frequency 0 1 2 3 4 5 6 7 8 9 10 11 or more than 11 19 14 15 9 14 6 4 2 2 3 2 0 (a) Estimate the average number of complaints received per day in the two different types of customer service where a customer is served by a Virtual Agent or not served by a Virtual Agent. Test the hypothesis that the average number of complaints received per day when served by a Virtual agent is the same the number of complaints received per day after not being served by a Virtual Agent at the 5% significance level (c) 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).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hi. Please help me with part A and C. Im stuck

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 5 6 35 12 13 11 Number of complaints received when not being served by a Virtual Agent Observed Frequency 0 1 2 3 4 7 8 9 10 11 more than 11 5 4 3 2 2 2 1 0 19 14 15 9 14 6 4 2 2 3 2 (a) Estimate the average number of complaints received per day in the two different types of customer service where a customer is served by a Virtual Agent or not served by a Virtual Agent. Test the hypothesis that the average number of complaints received per day when served by a Virtual agent is the the number of complaints received per day after not being served by a Virtual Agent at the 5% significance level (c) 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 5 6 35 12 13 11 Number of complaints received when not being served by a Virtual Agent Observed Frequency 0 1 2 3 4 7 8 9 10 11 more than 11 5 4 3 2 2 2 1 0 19 14 15 9 14 6 4 2 2 3 2 (a) Estimate the average number of complaints received per day in the two different types of customer service where a customer is served by a Virtual Agent or not served by a Virtual Agent. Test the hypothesis that the average number of complaints received per day when served by a Virtual agent is the the number of complaints received per day after not being served by a Virtual Agent at the 5% significance level (c) 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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