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A customer service department asks its customers to rate their​ over-the-phone service on a scale of​ 1-20 immediately after their service has been completed. The department then matches each​ customer's rating with the number of minutes the person waited on hold. The accompanying table shows the ratings and number of minutes on hold for 10 randomly selected customers.  Minutes Rating 4 16 9 13 0 19 5 11 7 14 2 15 9 14 4 20 8 15 4 12

A customer service department asks its customers to rate their​ over-the-phone service on a scale of​ 1-20 immediately after their service has been completed. The department then matches each​ customer's rating with the number of minutes the person waited on hold. The accompanying table shows the ratings and number of minutes on hold for 10 randomly selected customers.  Minutes Rating 4 16 9 13 0 19 5 11 7 14 2 15 9 14 4 20 8 15 4 12

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A customer service department asks its customers to rate their​ over-the-phone service on a scale of​ 1-20 immediately after their service has been completed. The department then matches each​ customer's rating with the number of minutes the person waited on hold. The accompanying table shows the ratings and number of minutes on hold for 10 randomly selected customers. 

Minutes Rating
4 16
9 13
0 19
5 11
7 14
2 15
9 14
4 20
8 15
4 12
 
Construct a​ 95% confidence interval for the average rating given by a customer who waits 14 minutes.
 
UCL=
LCL=
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c. Construct a 95% confidence interval for the average rating given by a customer that waits 1 minute. The formula for the confidence interval is given below, where y is the predicted value of y for the given value of x, t,/2 is the critical t-statistic from the Student's t-distribution with n- 2 degrees of freedom, s, is the standard error of the estimate, x is the average value of x from the sample, and n is the number of ordered pairs. (x-x)² 1 + (Ex)* (Ex²) - While technology or the formula can be used to find the confidence interval, in this problem, technology will be used. Before the confidence interval can be found, a few other calculations need to be done. The formula for y is given below, where bo is the y-intercept, b, is the slope, and x is the given value of x. y = bo + b,x Substitute the values x = 1, bo = 16.5662, and b, = - 0.3010 into the formula and simplify, rounding to three decimal places as needed. = bo + b,x = 16.5662 + (-0.3010) • 1 Substitute. = 16.265 Use technology to find the lower limit, rounding to two decimal places. LCL = 11.32 Use technology to find the upper limit, rounding to two decimal places. UCL = 21.21 Therefore, the 95% confidence interval for the average rating given by a customer who waits 1 minute has a lower limit of 11.32 and an upper limit of 21.21.
Transcribed Image Text:c. Construct a 95% confidence interval for the average rating given by a customer that waits 1 minute. The formula for the confidence interval is given below, where y is the predicted value of y for the given value of x, t,/2 is the critical t-statistic from the Student's t-distribution with n- 2 degrees of freedom, s, is the standard error of the estimate, x is the average value of x from the sample, and n is the number of ordered pairs. (x-x)² 1 + (Ex)* (Ex²) - While technology or the formula can be used to find the confidence interval, in this problem, technology will be used. Before the confidence interval can be found, a few other calculations need to be done. The formula for y is given below, where bo is the y-intercept, b, is the slope, and x is the given value of x. y = bo + b,x Substitute the values x = 1, bo = 16.5662, and b, = - 0.3010 into the formula and simplify, rounding to three decimal places as needed. = bo + b,x = 16.5662 + (-0.3010) • 1 Substitute. = 16.265 Use technology to find the lower limit, rounding to two decimal places. LCL = 11.32 Use technology to find the upper limit, rounding to two decimal places. UCL = 21.21 Therefore, the 95% confidence interval for the average rating given by a customer who waits 1 minute has a lower limit of 11.32 and an upper limit of 21.21.
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