ST 560 Midterm Exam - Untimed Component

Instructions: Show solutions in a neat and orderly manner. Answers to discussion questions should be brief and concise. If you need clarifications, please email your questions to the instructor. Do NOT post your questions on the Blackboard Learn Discussion Board. Using any resources other than the instructor, textbook, class notes, Excel or Minitab will be considered an act of academic misconduct.Submit your solutions via the Assignment labeled Midterm Exam.A full submission includes: one Word (or similar format) document.

The manager of a distribution center is concerned about delivery times associated with transporting materials to customers. In particular, deviations from the estimated travel time are of interest. Late arrivals cause financial penalties whereas early arrivals cause customer dissatisfaction due to congestion in the shipping areas and lost opportunity for the distribution center. A random sample of 100 recent deliveries is taken. The deviation in actual delivery time and estimated delivery time is calculated as Deviations = actual time estimated time.

1.A graphical summary is provided below. Give a brief description of the results.

2. If a calculated deviation (D) is positive, was the delivery late or early?

3. Each day hundreds of deliveries are scheduled. The manager decides to monitor the time deviations by taking a random sample of 25 deliveries and calculating the average deviation defined by for each day.Assume that historical data such as that displayed in

part (1) suggests that the distribution of deviations D_i have a mean of 5 minutes and a standard deviation of 10 minutes. Find the probability that the sample mean is negative.

(i.e. Find P[< 0] for a sample of size n=25).

4. A supervisor suggests that the old computer program for estimating delivery times (used in problems 1-3) be abandoned. Instead, schedulers could use an alternative such as MapQuest to estimate driving times. As a pilot study, 500 recent deliveries were randomly selected. The Excel file named Midterm 2017 Data.xls contains the following variables:

Actual Times actual time required to make delivery

Old Model Deviations difference in actual delivery time and predicted delivery time

using old computer prediction model

MapQuest predicted delivery times for the randomly selected routes using MapQuest

Use the data to calculate the deviations for the MapQuest estimates

(D_MapQuest = actual delivery time MapQuest predicted delivery time), then construct an appropriate graph for comparing the deviations for the Old Computer model and the MapQuest model. Interpret the results and indicate which prediction model should be used in the future. (Do NOT include the calculated deviations here. Do include the graph and interpretation.)

5. A driver reads your answer to part (4) and makes the following comment:

MapQuest gives driving times for cars. Driving times for trucks will probably be longer because we cant go as fast, especially in city traffic. Is there some way to adjust the MapQuest prediction to make it fit trucks better?

Construct a fitted line plot (scatterplot with fitted linear regression line) using the MapQuest times as the predictor variable and the actual times as the response variable. Call the regression values Adjusted MapQuest times. Provide the fitted line plot, regression equation and R² values associated with the Adjusted MapQuest times. Interpret your results and indicate whether the drivers suggestion is valid or invalid.

6.Use the regression equation given in part (5) to provide Adjusted MapQuest times for the sample of 500 deliveries and calculate the Adjusted Deviations = Actual times - Adjusted MapQuest times. (You do NOT need to put those values here.) Construct an appropriate graph for comparing the deviations associated with the Old Computer Model, the MapQuest model and Adjusted MapQuest model and include it here. Interpret the graph and recommend the modeling tool (method of predicting delivery times) you feel is most accurate.