Suppose that the average waiting time for a patient at a doctor's office is just over 29 minutes, and it is considered too long. The office manager would like to reduce patient waiting times to an average of 15 minutes. To address the issue of long patient waiting times, the office manager decides to introduce a wait-tracking system to notify patients of expected wait times using an app. Patients can adjust their arrival times based on this information and spend less time in the waiting room. Will introducing a wait-tracking system shorten wait times for patients? To answer this question, waiting times were recorded for a sample of patients before a wait-tracking system was introduced, and then for another sample of patients after a wait-tracking system was put in place. (a) (4 marks) Use EXCEL to obtain a histogram for patient waiting times with and without a wait- tracking system. EXCEL Instructions: Download the data file for this question, called Wait-Tracking.xlsx. Refer to Topic 6 in the Excel Booklet for instructions on how to obtain and edit a histogram; use the bins given in the data file. (b) (4 marks) Use EXCEL to obtain Descriptive Statistics, Quartile 1 (Q1) and Quartile 3 (Q3) for each distribution, wait times without a tracking system and wait times with a tracking system. EXCEL Instructions: Refer to Topic 7 in the Excel Booklet for instructions on how to obtain Descriptive Statistics and the two quartiles. (c) (12 marks) Based on the histograms in (a), briefly describe the shape (symmetry, modality and outliers) of the data distribution for each scenario. Instructions for identifying outliers: Whether an observation is an outlier is a matter of judgement. One rule commonly used for identifying outliers is the so-called 1.5 IQR rule. An observation is suspected to be an outlier if it lies more than 1.5 x IQR below the first quartile Q1 or above the third quartile Q3. Apply this rule to the data from each scenario. Identify suspected outliers (if any) by their exact value(s). (d) (6 marks) Nominate appropriate measures of centrality and dispersion for the distribution of waiting times with and without a tracking system. Give reason(s) for your choice. For each distribution, give and interpret the values of the summary measures you have chosen. (e) (4 marks) Consider the side-by-side boxplot shown below in Figure 1. What does it tell you about the distributions of patient waiting times with and without a wait-tracking system? Comment briefly on the shape and spread of the two distributions. (f) (4 marks) On the basis of your results of (a) to (d), are there any differences between waiting times with and without a tracking system? Are there any benefits of introducing a tracking system? (Hint: There are two benefits.) Is a wait-tracking system likely to help the office manager achieve the goal of an average patient waiting time of 15 minutes? Write a short report based on your findings to the practice manager (two to three paragraphs will be sufficient). Ensure that you quote relevant results in your report. Wait time (minutes) 70 60 50 40 20 10 2 Patient waiting times I Without Wait-Tracking With Wait-Tracking Figure 1. Side-by-side boxplots showing the distribution of patient waiting times with and without a wait-tracking system in place