# STAT1060: Business Decision

STAT1060: Business Decision Making

Assignment 2

This assignment must be submitted online

(via link on course schedule, see ‘Course Structure and Materials’)

before 10pm Sunday (22nd January 2017) Week 12

PLEASE READ – IMPORTANT INSTRUCTIONS – Including how to avoid loss of marks

? Contributes 15% towards your final grade.

? Examines lecture materials up to and including Lecture 11, and lab materials up to and including Lab 11 (Week 12). We suggest you DO NOT leave completion until too near the submission date, there are additional topics in Lecture 12 which you will also need to learn in preparation for the online quizzes and final exam.

? A completed ‘Assessment Item Cover sheet’ must be included with your submission

o by entering your details on the cover sheet and including with your online submission we will treat this as you having signed the sheet.

? Please read the course outline regarding assessments and penalties.

? Ensure you appropriately and accurately word your responses: review lecture and lab materials to assist.

? Show key steps leading to final results and include relevant SPSS output.

? SPSS is accessible on the university computers.

? Available marks are provided with each question. Total marks: 57

? You don’t need to repeat the text for each question in your response (but may do so if you prefer); however, you must clearly identify the question number and part to which you are responding.

Question 1 (6 marks)

Business, Management, Accounting, Finance, Economics, HR, OH&S, Law

As described on the Safe Work Australia website* a lost-time injury “… is defined as an occurrence that resulted in a fatality, permanent disability or time lost from work of one day/shift or more. This definition comes from the Australian standard: Workplace Injury and Disease Recording Standard (Australian Standard 1885.1– 1990), published by Standards Australia.”

*http://www.safeworkaustralia.gov.au/sites/swa/about/publications/pages/ns1990injuryanddiseaserecording

The table below provides causes of lost-time injuries, and their relative frequency (percentage) of occurrence, across the previous two years at a mining site.

Cause Percentage

Vehicle Accident 4

Fall/slip on same level 25

Fall from height 3

Hit by falling object 31

Pushing/pulling object 5

Contact with chemical 5

Cut by tools 14

Exposed to mental stress 4

Other mechanisms 9

100

The data are also available in the file ‘Assignment 2 Q1 – Tri 3 2016.sav’ available in the list of SPSS files on Blackboard (under Resources/HELP).

a) Create and provide the appropriate chart for the data provided.

[2 marks]

b) Write a brief report of your findings. NOTE: A comprehensive response should require less than 100 words.

[4 marks]

Question 2 (17 marks)

Management, Accounting, Finance, HR, Business Performance

In many service-based organisations, such as accounting firms, performance appraisals of employees are based on the individual’s number of ‘chargeable hours’ of work to clients for the period in question. Senior partners within a particular accounting firm wanted to assess the performances of two groups of their accountants. One group was represented by their more-recently recruited graduate students, the second was represented by their more highly-paid employees who have completed the additional qualification of becoming a certified practicing accountant. The organisation was interested in, amongst many measures of performance, assessing whether the differences in salary could be justified by differences in chargeable hours.

The firm selected a random sample of 20 days from the past quarter (3-month period) and 6 accountants from each group and recorded the daily numbers of chargeable hours to clients for each of the individuals on those days. This resulted in 120 observations for each group.

The two groups are referred to as CPA and non-CPA employees.

The data are provided in the file named ‘Assignment 2 Q2 – Tri 3 2016.sav’ available in the list of SPSS files on Blackboard (under Resources/HELP).

a) One key variable is Employee type, with possible responses being CPA or non-CPA. The second key variable is daily chargeable hours (abbreviated hereafter to Chargeable hours). Identify each variable’s type, and give a brief clear reason for your decision.

[2 marks]

b) Use SPSS to construct a histogram for all Chargeable hours. How would you describe the shape? Include your histogram.

[2 marks]

c) Use SPSS to construct separate histograms of Chargeable hours for each of the CPA and non-CPA employees. You must also perform the following on the histograms:

? Use a common scale for both histograms: set a minimum of 0 and a maximum of 10;

? Change the width of the bins (intervals) to 0.6;

? Vertically align the two histograms (paste one directly below the other) when including in your submission.

[2 marks]

d) What other graphical presentation would be useful to compare the Chargeable hours for the CPA and non-CPA employees? Name and provide the visual display using SPSS.

[2 marks]

e) Use SPSS to find the mean, median, standard deviation and interquartile ranges of the Chargeable hours for the CPA employees. Repeat for the non-CPA employees. Do not simply include raw output.

[2 marks]

f) Identify why it would be suitable to use all of the above four summary measures to describe the distribution of Chargeable hours.

[1 mark]

g) Using your output created in parts (b) – (e), give a brief report comparing the Chargeable hours for the CPA and non-CPA employee groups.

[4 marks]

h) The Senior Partners of the firm believe CPA employees should be achieving at least 8 chargeable hours per day.

i. Use the empirical rule to (approximately) estimate the probability of this minimum number of Chargeable hours being achieved. Show your working. Do NOT use the computer to get a more accurate answer.

NOTE: round the mean and standard deviation you obtained earlier to 2 decimal places before using them to estimate the probability via the empirical rule.

[1 mark]

ii. Does it appear the Senior Partners’ expectations are being met? Explain.

[1 mark]

Question 3 (23 marks)

Management, Logistics and Supply Chain, Process Control, Finance, Accounting

Quality control is an important part of the manufacturing process, helping to ensure consumers receive products which are to their satisfaction. The consequences of poor quality products include, but are not limited to, issues of reputation, non-repeat purchases, costs of repairs under warranty, costs of scrap and rework of materials; this affects the company’s finances and potential future existence.

The assembly of free-standing DIY bookshelves involves the connection of shelves to the main frame of the bookcase. The shelves and bookcase have slots/holes into which short connector ‘rods’ (dowel) must fit. An example image is available at the link below**.

A particular supplier of these bookshelves has specifications that include the requirement that the mean diameter of the connector ‘rods’ is 14.0mm, otherwise shelves will be either too loose, or the rod will not easily fit within the slot/hole. The diameters of a random sample of 35 rods from this supplier are provided in the file named ‘Assignment 2 Q3 – Tri 3 2016.sav’ available in the list of SPSS files on Blackboard (under Resources/HELP).

**For an image of connector ‘rods’ click here:

a) Use SPSS to obtain a 95% confidence interval for the mean diameter of the connector rods.

i. State the 95% confidence interval (i.e., simply give the lower & upper limits), and include the SPSS output from where you obtained the interval.

[2 marks]

ii. Interpret the 95% confidence interval (i.e., give a statement) relating it to the context of the scenario. Reminder: ensure you accurately word your response.

[4 marks]

iii. Explain, using support from the 95% confidence interval, what you would conclude about the supplier meeting the specification requirement. Reminder: ensure you accurately word your response.

[5 marks]

b) Use SPSS to conduct a formal hypothesis test, using a 5% significance level, of whether the mean diameter of the connector rods is meeting the specification requirement (14.0mm). Apply the five steps that were outlined in the lecture and include the SPSS output from where you obtain the p-value. Reminder: Ensure the marker can understand any decisions you make.

[12 marks]

Question 4 (11 marks)

Management, Accounting, Finance, HR, Business Performance

Recall Question 2 – The following questions apply to that same scenario and data set

a) Use SPSS to obtain a 95% confidence interval for the difference in the mean chargeable hours for CPA and non-CPA employees.

i. State the 95% confidence interval (i.e., simply give the lower & upper limits) and include the SPSS output from where you obtained the interval.

[2 marks]

ii. Interpret the 95% confidence interval (i.e., give a statement) relating it to the context of the scenario. Reminder: ensure you accurately word your response.

[4 marks]

b) Prior to the above analysis, a CPA employee had commented that, based on her experience at other organisations she expected a difference in mean chargeable hours per day of 3.5. Explain, using support from the 95% confidence interval, what you would conclude about such a comment. Reminder: ensure you accurately word your response.

[5 marks]

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