Barbara Dwyer, the manager at Lux Hotel, makes every effort to ensure that customers attempting to make phone reservations wait an average of only 60 seconds to speak with a reservations specialist. She knows that this is likely to be the customer's first impression of the hotel and she wants the initial interaction to be a positive one. Since the hotel accepts phone reservations 24 hours a day, Barbara wonders if the quality of service is consistently maintained throughout the day. She takes six samples of n = 4 calls during each of four shifts over one 24-hour period and records the wait time of each call. A portion of the data, in seconds, is presented in Table 7.2. Barbara assumes that wait times are normally distributed with a mean and standard deviation of 60 seconds and 30 seconds, respectively. She wants to use the sample information to construct a control chart for wait times. Using the control chart, she then wants to determine if the quality of service is consistently maintained throughout the day. FILE Lux_Hotel TABLE 7.2 Wait times for phone reservations Shift Shift 1: 12:00 am-6:00 am Sample 1 Wait Time (in seconds) Sample Mean, X 67 48 52 71 60 2 57 68 60 66 63 3 37 41 60 41 45 4 83 59 49 66 64 5 82 63 64 83 73 16 87 53 66 69 69 B Shift 4: 6:00 pm-12:00 am 19 6 11 8 9 9 20 10 8 10 9 9 21 11 7 14 7 10 22 8 9 9 12 23 9 12 9 14 24 5 8 15 11 241 10 11 10 Sample Report-Customer Wait Time When a potential customer phones Lux Hotel, it is imperative for the reservations specialist to set a tone that relays the high standard of service that the customer will receive if he/she chooses to stay at the Lux. For this reason, management at the Lux strives to minimize the time that elapses before a potential customer speaks with a reservations specialist; however, management also recognizes the need to use its resources wisely. If too many reservations specialists are on duty, then resources are wasted due to idle time. Yet, if too few reservations specialists are on duty, then the result might be unhappy customers, or worse. In order to ensure customer satisfaction as well as an efficient use of resources, a study is conducted to determine whether a typical customer waits an average of 60 seconds to speak with a reservations specialist. Before data are collected, a control chart is constructed. The upper control limit (UCL) and the lower control limit (LCL) are set three standard deviations from the desired average of 60 seconds. Figure 7.13 shows the control chart where the centerline is at 60 seconds and the UCL and the LCL are at 105 seconds and 15 seconds, respectively. The reservation process is deemed under control if the sample means fall randomly within the control limits; otherwise, the process is out of control and adjustments should be made. FIGURE 7.13 Sample mean wait times 140 120 100 80 60 40 20 0 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 Sample number 24 Centerline = 60 UCL = 105 LCL = 15 Sample means

Barbara Dwyer, the manager at Lux Hotel, makes every effort to ensure that customers attempting to make phone reservations wait an average of only 60 seconds to speak with a reservations specialist. She knows that this is likely to be the customer's first impression of the hotel and she wants the initial interaction to be a positive one. Since the hotel accepts phone reservations 24 hours a day, Barbara wonders if the quality of service is consistently maintained throughout the day. She takes six samples of n = 4 calls during each of four shifts over one 24-hour period and records the wait time of each call. A portion of the data, in seconds, is presented in Table 7.2. Barbara assumes that wait times are normally distributed with a mean and standard deviation of 60 seconds and 30 seconds, respectively. She wants to use the sample information to construct a control chart for wait times. Using the control chart, she then wants to determine if the quality of service is consistently maintained throughout the day. FILE Lux_Hotel TABLE 7.2 Wait times for phone reservations Shift Shift 1: 12:00 am-6:00 am Sample 1 Wait Time (in seconds) Sample Mean, X 67 48 52 71 60 2 57 68 60 66 63 3 37 41 60 41 45 4 83 59 49 66 64 5 82 63 64 83 73 16 87 53 66 69 69 B Shift 4: 6:00 pm-12:00 am 19 6 11 8 9 9 20 10 8 10 9 9 21 11 7 14 7 10 22 8 9 9 12 23 9 12 9 14 24 5 8 15 11 241 10 11 10 Sample Report-Customer Wait Time When a potential customer phones Lux Hotel, it is imperative for the reservations specialist to set a tone that relays the high standard of service that the customer will receive if he/she chooses to stay at the Lux. For this reason, management at the Lux strives to minimize the time that elapses before a potential customer speaks with a reservations specialist; however, management also recognizes the need to use its resources wisely. If too many reservations specialists are on duty, then resources are wasted due to idle time. Yet, if too few reservations specialists are on duty, then the result might be unhappy customers, or worse. In order to ensure customer satisfaction as well as an efficient use of resources, a study is conducted to determine whether a typical customer waits an average of 60 seconds to speak with a reservations specialist. Before data are collected, a control chart is constructed. The upper control limit (UCL) and the lower control limit (LCL) are set three standard deviations from the desired average of 60 seconds. Figure 7.13 shows the control chart where the centerline is at 60 seconds and the UCL and the LCL are at 105 seconds and 15 seconds, respectively. The reservation process is deemed under control if the sample means fall randomly within the control limits; otherwise, the process is out of control and adjustments should be made. FIGURE 7.13 Sample mean wait times 140 120 100 80 60 40 20 0 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 Sample number 24 Centerline = 60 UCL = 105 LCL = 15 Sample means

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 23PPS

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