6. Customers who call Cox Communications customer service line must wait until a representative is available to answer t
Posted: Wed May 11, 2022 8:33 am
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6. Customers who call Cox Communications customer service line must wait until a representative is available to answer the phone call. The CEO is interested in the mean customer wait time. An SRS of thirteen calls were selected and their wait time was recorded. The histogram of the 13 times is displayed below. Frequency 0 0.5 3.0 1.0 1.5 2.0 2.5 Wait Time (minutes) (a) Based on this graph, explain why it might not be appropriate to use a one-sample t-interval to estimate the average time spent waiting for all customers. Statisticians regularly use logarithmic transformations for this type of data. Let x represent a customer's time spent waiting. The log of the Cox customers' wait times is given below. The corresponding means, medians, and standard deviations are also shown. Wait Time, X 0.40 0.66 0.71 0.71 1.10 1.16 1.20 1.29 1.29 1.70 1.90 2.15 2.82 1.31 1.20 0.679 log10* -0.3979 -0.1805 -0.1487 -0.1487 0.0414 0.0645 0.0792 0.1106 0.1106 0.2304 0.2788 0.3324 0.4502 0.0632 0.0792 0.235 Mean Median Standard deviation A histogram of the 13 logged data values is shown below. Frequency -0.3 -0.1 0.1 0.3 0.5 Log of Wait Time (log10 minutes)
The summary statistics for x and x are repeated below. Mean Median Standard deviation Wait Time, x 1.31 1.20 0.679 log10 x 0.0632 0.0792 0.235 (b) Construct and interpret a 95 percent confidence interval for the population mean u of the log of the wait times. Assume the conditions for inference have been met. (c) The mean of the logged data is 0.0631 log10 minutes, which can be converted back to 1.156 minutes by calculating 10 . Convert the endpoints of your interval in part (b) back to minutes and write the resulting interval. 100.0631 Graph 1 below shows a population distribution of the log of time spent waiting, which is normal with mean u. Graph 2 shows the result of converting the population distribution in Graph 1 back to the population distribution of time spent waiting. The lower half of the distribution is shaded in each graph. Graph 1 Population Distribution of Log of Wait Time Graph 2 Population Distribution of Wait Time 0.5 0.5. log10 u 104 (d) Consider the parameter 10" in Graph 2. (i) How does the value of 10" compare with the median of the population distribution of wait times? (ii) How does the value of 10" compare with the mean of the population distribution of wait times? (e) Write an interpretation of the interval you constructed in part (C).