Needs to be solved in Minitab
Midterm Exam Maximum points: 200 Due date: Before the Week 6 live session Instructions: • This is an open-book, open-notes, open-internet INDIVIDUAL exam. No part of this exam should be discussed or worked on in groups. • If you need clarification on any part of a question on this exam, please contact me. • The solved examples on my videos and notes and the homework/live session exercises will be serve as the best aid. • For the Simple Linear Regression question, you might want to consider following my COMMNODES Solved Example. It should be available on the course website under the file COMMNODES Exercise – SOLVED. • Please paste your Minitab outputs neatly on this document for each question. • There are five (5) questions, each having multiple parts. Please answer all the questions to be considered for full credit. Please read and sign. I understand that if I discuss this exam with anyone or seek external help, I will be in violation of the Honor Code and may face serious penalties as decided by the University. Name: _____________________ Date: ___________________ Page 1 of 4 (40 points) Question 1 A study is performed on a sample of residential homes to discover whether the size of the monthly heating bill depends on the type of heat or the type of home. In particular, three types of heat are examined: electric, natural gas, and oil. Also, all homes are classified into two types: those on a single level and those with at least two stories. In a single community, 10 houses of each type, using each type of heat, are located and their heating bills for February of the past year are observed. These STACKED data are listed in the Minitab file Question 1. Assume that the homes in this study are approximately equivalent in terms of overall square footage and level of insulation. Type of Heat Electric Natural Gas Oil Home Type Single $148.03 $131.97 $140.18 Single 143.78 134.67 135.04 Single 142.19 131.28 138.61 Single 144.14 138.69 141.83 . . . . . . . . . . . . Two-storied or more 149.99 133.14 141.78 Two-storied or more 141.86 132.65 139.24 Two-storied or more 144.19 130.98 142.44 Two-storied or more 149.10 122.60 145.36 . . . . . . . . . . . . Using a 5% significance level, answer the questions below. Assume the normality and equal variance conditions are met, so do not run any diagnostics. A. (1 point) How many factors are there? B. (1 point) What are the levels of each factor? C. (1 point) How many treatments are there? Page 2 of 4 D. (1 point) What is the response variable? E. (16 points) Determine if there is any interaction between heat type and home type when explaining the variation in monthly heating bill. Show an interaction plot and verify your conclusion from the ANOVA output. F. (10 points) Test whether or not the monthly heating bill differs by heat type. G. (10 points) Test whether or not the monthly heating bill differs by home type. (40 points) Question 2 Caterpillar, Inc. manufactures and sells heavy construction equipment worldwide. The performance of Caterpillar’s stock is likely to be strongly influenced by the economy. For instance, during the subprime mortgage crisis, the value of Caterpillar’s stock plunged dramatically. Monthly data for Caterpillar’s risk-adjusted return (? − ??) and the risk-adjusted market return (?? − ??) are collected for a five-year period (? = 60). The dataset is shown on the Minitab file Question 2. A. (10 points) Estimate the CAPM model for Caterpillar, Inc. Show the regression results. B. (20 points) At the 5% significance level, determine if investment in Caterpillar stock is riskier than investing in the market. Please write your hypotheses clearly. C. (10 points) At the 5% significance level, is there evidence of abnormal returns? Please write your hypotheses clearly. (15 points) Question 3 To determine whether the satisfaction rating of an airline differs between business class and economy class, a survey was performed. Random samples of both groups were asked to rate their satisfaction with the quality of service using the following responses: Very satisfied Quite satisfied Somewhat satisfied Neither satisfied nor dissatisfied Somewhat dissatisfied Quite dissatisfied Very dissatisfied Using a 7-6-5-4-3-2-1 coding system, the results were recorded. Can we infer that business and economy class differ in their degree of satisfaction with the service? The dataset is shown on the Minitab file Question 3. Page 3 of 4 (25 points) Question 4 A large corporation sends many of its first-level managers to an offsite supervisory skills training course. Four different management development centers offer this course. The director of human resources would like to know whether there is a difference among the quality of training provided at the four centers. An independent random sample of five employees was chosen from each training center. The employees were then ranked 1 to 20 in terms of supervisory skills. A rank of 1 was assigned to the employee with the best supervisory skills. The ranks are shown on the Minitab dataset Question 4, which are available in both STACKED and UNSTACKED formats. At the 5% significance level, can we conclude if there is a significant difference among the quality of training provided by the four programs. Please don’t forget to write the hypotheses after you identify the appropriate test to run. (80 points) Question 5 Before taking the plunge into videoconferencing, a company ran tests of its current internal computer network. The goal of the tests was to measure how rapidly data moved through the network given the current demand on the network. Eighty files ranging in size from 20 to 100 megabytes (MB) were transmitted over the network at various times of day, and the time to send the files (in seconds) was recorded. The data are available on Minitab file Question 5. Using Transfer Time as the response variable (dependent variable) and File Size as the predictor (independent variable), complete the following tasks: A. (5 points) Create a scatterplot and determine the strength of correlation. B. (5 points) Find the correlation coefficient and determine the strength of correlation. C. (10 points) Using the inference regarding population correlation, determine whether the correlation in the population is statistically significant. D. (10 points) Paste the sample regression equation from Minitab. Interpret the slope. E. (10 points) Is there sufficient evidence to conclude that a linear relationship exists between Transfer Time and File Size? Use the test for slope to answer this question. F. (5 points) Find and interpret the 95% confidence interval estimate for ?1. G. (10 points) Test whether there is a positive correlation between File Size and Transfer Time. H. (5 points) What percentage of variation in Transfer Time is explained by the regression? I. (10 points) Use the ?-test to determine whether the Transfer Time and File Size are linearly related. Page 4 of 4 J. (10 points) A claim has been made that each increase in file size by 1 MB adds less than 0.5 second to the transfer time. Test this claim by using the test of ?1.