Refer to the chapter-opening Case Study on page 475. The bank manager wants to know whether or not the bank’s customer ser vice 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 an swered within 30 seconds or by estimating the mean response time m. Some graphs and numerical summaries of the data are provided below. Questions: 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. (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. Please answer all questions
Refer to the chapter-opening Case Study on page 475. The bank
manager wants to know whether or not the bank’s customer ser
vice 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 an
swered within 30 seconds or by estimating the mean response
time m.
Some graphs and numerical summaries of the data are provided below.
Questions:
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.
(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.
Please answer all questions
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