ACCG615 Quantitative Methods

This assignment must be completed in a group of three or four students. Initially, each student should attempt the entire assignment independently. As each part of this assignment covers various sections from the unit it is important that each student attempts all questions. The purpose of group work is to give students an opportunity to work together as a team by discussing their solutions. Under no circumstances should each student in the group attempt only part of the assignment.

• Only one assignment should be submitted per group.
• Assignment solutions should initially be typed up as a word processed document, with relevant MINITAB output cut and pasted into the document. You will then need to sign this cover sheet and attach it to the front of your assignment to be scanned and converted to a PDF document. This document will then need to be uploaded to iLearn as a PDF file.
• No submissions will be accepted by email or other means.
• When you think you have submitted your Assignment, please check to make sure: in iLearn, click on the assignment and you should see your uploaded file. Check also that it uploaded correctly (and that you uploaded the correct file) by clicking on the submission. You will also receive an email notifying you of your submission if uploaded correctly.
• Students should only work with other students in their group. Evidence of collusion between groups, as indicated by similar assignments, will result in zero marks.

Please complete the information below. Each student in the group is expected to contribute equally to the assignment and each will receive the mark allocated for the assignment.

The total mark for the assignment is 50. Marks will be awarded for neatly presented assignments.

Please note the following penalties for late assignments will apply:

20% (10 marks) deduction for submissions up to 1 hour late

50% (25 marks) deduction for submissions more than 1 hour and up to 24 hours late No submissions will be accepted more than 24 hours after the due date and time.

Please read the section regarding presentation of your assignment on the following page before you start to write up your assignment.

Marks will be deducted for poor presentation. Full marks for presentation will not be awarded if any of the following points are not taken into account in writing up your assignment.

• Your assignment must be word-processed and saved as a pdf file with the cover page scanned and attached. WORD files will not be marked.
• Each question (and each part of each question) must be clearly numbered and the solution must be presented in the correct order.
• Where MINITAB is cut and pasted into your solution:
  • Do not include output that is not relevant. o All output must be clearly labelled with meaningful titles/labels. o Graphs should be resized appropriately.
  • Output which is cut and pasted into your solution must line up neatly – output that wraps around the page is meaningless.
  • Do not have computer output running over two pages. Page breaks in the middle of computer output are unacceptable.
• Where possible, do not have parts of questions running over two pages Adhere to the page limits specified for each question.

Use a significance level of 5% for all hypothesis tests in this assignment except where otherwise indicated. Question 1 (15 Marks)

Research Question: Are there significant differences between the average weekly cost of owning and operating petrol cars, electric cars, SUVs and utility vehicles?

You should address the Research Question outlined above. Your answer to this question should consist of two word-processed pages presented in the form of a statistical report. The report as outlined below should be provided on the first page with any appropriate MINITAB output provided on the second page.

A motoring organisation conducted a study to compare the average weekly costs of owning and operating various types of vehicles for private purposes. 121 vehicles were included in the study. Each vehicle belonged to one of four different classes – petrol car, electric car, SUV or utility vehicle. The cost of running each vehicle for one week was recorded. Weekly costs included depreciation, registration, insurance, servicing and either electricity or fuel (assuming each vehicle travelled 15000 km annually). As well as determining whether any differences exist your report should also outline the results of any appropriate multiple comparisons you have made and the reason for choosing this method of multiple comparisons. Use an overall significance level of 6% for this question.

Directions for report writing are given below. More information on report writing, as well as a sample report is provided on iLearn in the Resources folder. Use the MINITAB file CarCosts.mtw to answer this question. There is a two page limit on this question.

Introduction: State the research question and any background information including why the study is being conducted. The target population should be made clear.

Methods: Provide a description of the sample used and the variable/s considered. Indicate the statistical test being used and the reason for using it. This should also include a comment on the underlying assumptions of the test. Mention any concerns. If the study is experimental, the design of the experiment should be outlined.

Results: Outline the results from your analyses including the test statistic/s and p-value/s. You should also clearly state whether or not your result/s are statistically significant.

Conclusion: This should summarise the overall findings of your study. It should address the research question and include any appropriate confidence intervals.

Question 2 (14 marks)

Monash University undertook a study into factors involved in motor vehicle accidents. The study examined various conditions at the time of more than 1100 motor vehicle accidents which had occurred in New Zealand the previous year. The MINITAB file accidents.mtw summarises the results for the time of day when each accident occurred and the age of the driver at the time of each accident.

Note: WeekDay-Day = Monday to Friday during daylight hours, WeekEnd-Day = Saturday or

Sunday during daylight hours, WeekDay-Night = Monday to Friday nights, WeekEnd-Night = Saturday or Sunday nights. Please note that there is a two page limit on this question.

Source: The Risk of Driver Crash Involvement as a Function of Driver Age, A. E. Drummond and E. Y. Yeo, 1992,

Monash University Accident Research Centre (adjusted)

1. Previous research indicated that 55% of motor vehicle accidents occurred on weekdays during daylight hours, 13% occurred on weekends during daylight hours, 14% occurred on weekdays during the night and the remainder occurred on weekends during the night. Using a 5% significance level, carry out an appropriate hypothesis test to determine whether there is evidence that these proportions have changed.
2. Now carry out an appropriate hypothesis test, at a 5% significance level, to determine whether there is any association between the time of day motor vehicle accidents occur and the age of the driver.

Question 3 (16 marks)

An Energy study was conducted over a six year period to investigate factors which could be used to predict the net hourly energy output of a power plant. The data are from a randomly selected sample of 500 observations recorded during the course of the study. Use the MINITAB file energy.mtw to answer this question. Each observation consists of information recorded on the following variables.

Variable Description

AirTemp Hourly average air temperature (°C) AirPressure Hourly average air pressure (millibars)

RelHumidity Hourly average relative humidity (%)

Energy Net hourly electrical energy output (megawatts)

1. Using a scatter plot matrix (matrix plot) and/or a correlation matrix, answer the following questions giving the units of measurements where appropriate:
   1. What was the approximate relative humidity when the highest energy output was observed?
   2. Which predictor is most strongly related to energy output? iii. Using _α = 0.05, which predictor/s are significantly related to energy output? iv. Using _α = 0.01, which predictors are significantly related to each other?
   3. Calculate the coefficient of determination for the relation between energy output and air pressure and write a sentence interpreting this value.
2. Carry out a global test to determine whether any of the potential determinants listed above are useful for predicting the energy output of a power plant. Use a 5% significance level to conduct this test.
3. Using an appropriate model reduction process determine which, is the best model for predicting energy output using a 5% significance level? Write out this model.
4. Interpret the coefficient of any one of the variables in the final model you selected in part c.
5. Use the model you chose in part c. to predict the energy output for a power plant when the air temperature is 20 degrees C, the air pressure is 1000 millibars and the relative humidity is 75%.