[SOLVED] R statistic OPIM 5603 Statistics in Business Analytics

OPIM 5603 Statistics in Business Analytics
Homework Assignment #6 Due on October 25, 2019
This assignment is team work; students are allowed to work with one partner. Submit your answers in one Word file attachment via Husky CT, no later than 11:59 p.m. on the due date. Make sure your Word document contains your written answers to all the required computations and questions. Also include in the Word file the corresponding R code you used to answer the questions (if any). By submitting the assignment, you are confirming that this represents your teams work, and that no part of the work submitted has been copied from other teams. Consequences for cheating can be quite serious. It can lead to not only failing the course but also dismissal from the program. If determined that more than two students have worked on the same assignment submission, the participants will only get a fraction of the assignments grade.
Problem: The residents of several communities near Palo Alto, California, have complained about the poor shuttle service between their communities and Town & Country Shopping Center, a nearby mall. To attract more customers, Town & Countrys management had recently started free hourly shuttle services to the surrounding communities; each community has an assigned shuttle that departs at the start of each hour, beginning at 9 a.m. and ending at 7 p.m. Bill Chen, one of the managers, is taking care of the complaints. Apparently, the residents of those communities are not satisfied with the long time it takes a one-way trip from their respective communities to the mall. The shuttle schedule sheet states that a one- way trip from any community to the mall should take about 20 minutes. Nevertheless, many residents claim that it takes 35 minutes or more on the average! To determine whether or not there is some truth in the complaints, Bill has collected a sample of the duration (in minutes) of one-way trips from each of the eight communities to the mall during the last 20 working days. The observations can be found in the Excel file entitled PaloAlto.xlsx available on Husky CT. Perform the following tasks in R Studio:
Task 1. Compute the mean, median, range, sample standard deviation, skewness, kurtosis and coefficient of variation of the travel times for each community (Hint: use the tapply function). Comment on the dispersion for each community. Identify which communities have the highest and lowest dispersion in travel time. Create a data frame with eight rows and three columns whose first column is the names of the communities, the second column is the mean travel time of each community, and the third column is the standard deviation of the travel time each community. Refer to this frame as CommFrame.
Task 2. Compute 95% confidence intervals for the average travel time for each community. Using the confidence intervals, compute the margin of error for the travel time of each community. For each community, determine the sample size required to achieve a margin of error of at least 0.1 minutes with a 99% confidence level. Include your results in the CommFrame by adding the necessary columns for the confidence intervals, margin of error, and target sample size. Display the final frame on the Word document.

OPIM 5603 Statistics in Business Analytics
Task 3. For the East Palo Alto community, compute the average travel time for each hour. Create a plot showing how the averages per hour change as time goes from 9 a.m. to 7 p.m. The horizontal axis must show the hourly times in correct sequence: 9 a.m., 10 a.m., 11 a.m., , 7 p.m. (you would probably need to research how to do this on the web). Repeat the same process for the other seven communities.
Task 4. For each community provide a 93% confidence interval for the true proportion of trips that take more than 20 minutes. In doing so, for each community check first whether the sample is large enough and if it is not, then do not compute the interval. Also, for each community determine the sample size required to attain a 1% margin of error for this proportion with a 95% confidence.
Task 5. For each community determine whether there is statistical evidence to support the residents complaints and write down your conclusion, solely use the confidence intervals for the mean to do this (do not use hypothesis testing). By visually examining the plots from Task 3, for each community identify any patterns that could explain the longer travel times and explicitly describe in words the pattern (if any). Based on all your analysis, provide at least three managerial recommendations addressed to Bill on how to deal with the customers complaints (justified or not); carefully think what you recommend because shallow or repetitive recommendations will receive not credit.