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4. Construct and interpret a 95% confidence interval for the true mean response time of calls to the bank's customer service center. 5. Is the customer service center meeting its goal of answering calls in less than 30 seconds? Give appropriate evidence to support your answer.

4. Construct and interpret a 95% confidence interval for the true mean response time of calls to the bank's customer service center. 5. Is the customer service center meeting its goal of answering calls in less than 30 seconds? Give appropriate evidence to support your answer.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 25SGR
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Can you answer questions 4 and 5?
(d) Interpret the interval from part (c) in context. 4. Construct and interpret a 95% confidence interval for the true mean response time of calls to the bank's customer service center. 5. Is the customer service center meeting its goal of answering calls in less than 30 seconds? Give appropriate evidence to support your answer.
Transcribed Image Text:(d) Interpret the interval from part (c) in context. 4. Construct and interpret a 95% confidence interval for the true mean response time of calls to the bank's customer service center. 5. Is the customer service center meeting its goal of answering calls in less than 30 seconds? Give appropriate evidence to support your answer.
case closed Need Help? Give Us a Call! Refer to the chapter-opening Case Study on page 000. The bank manager wants to know whether or not the bank's customer service agents generally met the goal of answering incoming calls in less than 30 seconds. We can approach this question in two ways: by estimating the proportion p of all calls that were answered within 30 seconds or by estimating the mean response time µ. Some graphs and numerical summaries of the data are provided below. 35 25- 15- Call response time (seconds) 00 7,5 15.0 22.5 30.0 37.5 45.0 Call response time (seconds) Descriptive Statistics: Call response time (sec) Variable N Мean SE Mean StDev Minimum Q1 18.353 11.761 1.000 9.000 Call response time (sec) 241 0.758 1. Describe the distribution of call response times for the random sample of 241 calls. 2. About what proportion of the call response times in the sample were less than 30 seconds? Explain how you got your answer. 3. The bank’s manager would like to estimate the true proportion p of calls to the bank’s customer service center that are answered in less than 30 seconds. (a) What conditions must be met to calculate a 95% confidence interval for p? Show that the conditions are met in this case. (b) Explain the meaning of 95% confidence in this setting. (c) A 95% confidence interval for p is (0.783, 0.877). Give the margin of error and show how it was calculated.
Transcribed Image Text:case closed Need Help? Give Us a Call! Refer to the chapter-opening Case Study on page 000. The bank manager wants to know whether or not the bank's customer service agents generally met the goal of answering incoming calls in less than 30 seconds. We can approach this question in two ways: by estimating the proportion p of all calls that were answered within 30 seconds or by estimating the mean response time µ. Some graphs and numerical summaries of the data are provided below. 35 25- 15- Call response time (seconds) 00 7,5 15.0 22.5 30.0 37.5 45.0 Call response time (seconds) Descriptive Statistics: Call response time (sec) Variable N Мean SE Mean StDev Minimum Q1 18.353 11.761 1.000 9.000 Call response time (sec) 241 0.758 1. Describe the distribution of call response times for the random sample of 241 calls. 2. About what proportion of the call response times in the sample were less than 30 seconds? Explain how you got your answer. 3. The bank’s manager would like to estimate the true proportion p of calls to the bank’s customer service center that are answered in less than 30 seconds. (a) What conditions must be met to calculate a 95% confidence interval for p? Show that the conditions are met in this case. (b) Explain the meaning of 95% confidence in this setting. (c) A 95% confidence interval for p is (0.783, 0.877). Give the margin of error and show how it was calculated.
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