Midterm Exam - Untimed Component

Answers to discussion questions should be brief and concise.

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 16 deliveries and calculating the average deviation defined by D^- = 1/16 _i=1∑¹⁶ D_i 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 27 minutes and a standard deviation of 20 minutes. Find the probability that the sample mean is less than 15 minutes. (i.e. Find P[D^- < 15] for a sample of size n=16).

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 2018 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

(DMapQuest = 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 can't 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 fitted 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 driver's 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.

Attachment:- Data File.rar