(1) For part 2, a file named “Assignment Data Sets”, containing the data sets for the questions, can be downloaded from the e-learning site vUWS. You should find and download the data set for your group.
(2) You should use Excel to carry out all calculations and statistical analyses. Students should consult the Excel handout which can be found on vUWS
(3) To complete this assignment, you must provide the Excel outputs for each of the questions in a report.
(4) Your assignment submitted must be typed and word-processed.
(5) The maximum number of pages for each submission is six (6), not including the cover page. No mark will be given if the number of pages exceeds the limit.
(6) The assignment is to be submitted online by the team leader before 5pm , the day after your tutorial in Week 13
(7) Any late assignments will be penalised 10% of the total mark per day
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Part 1 – 10 marks
Question 1 (3 + 2 = 5 marks)
A small independent general practice has three doctors. Dr Smith sees 40% of the patients, Dr Tran sees 30% and Dr Jackson sees the rest. Dr Smith requests blood tests on 5% of her patients, Dr Tran requests blood tests on 8% of his patients and Dr Jackson requests blood tests on 6% of her patients.
An auditor from the Australian Health Insurance Commission randomly selects a patient from the past week;
a) What is the probability that the selected patient had a blood test as a result of a visit to the general practice?
b) What is the probability that given the selected patient had a blood test as a result of a visit to the general practice; they were seen by Dr Smith?
Question 2 (2 + 3 = 5 marks)
The lifetime of a certain brand of light bulb is normally distributed, with a mean of 7500 hours and a standard deviation of 700 hours.
a) If the light bulbs carry a warranty for 6000 hours, what proportion of the bulbs will fail before the warranty expires?
b) The manufacturer replaces for free all bulbs that fail while under warranty. If they are willing to replace 2% of light bulbs that fail, what warranty should they offer?
Part 2 – 20 marks
The Minister of Industry and Trade is interested in the characteristics of local businesses. He decides to concentrate on businesses in the Parramatta CBD and the Sydney CBD. He employees a research company to survey 70 local businesses. This was carried out and the following variables recorded.
Column 1 Profit What was your profit?
Column 2 Type Is the business privately held, publicly traded or a franchise? (Private = 1, Public = 2, Franchise = 3)
Column 3 Employee How many employees work at your business?
Column 4 Age How old is the company (in years)?
Column 5 Location Where is the company? (1 = Parramatta CBD, 2 = Sydney CBD)
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Question 3 (5 marks)
Calculate a 95% confidence interval for the unknown population mean business age.
Question 4 (5 marks)
Test, at the 1% level of significance, whether the average business has more than 15 employees.
Question 5 (5 marks)
Test, at the 5% level of significance, whether the average profit in 2014 differs between businesses located in Parramatta CBD or located in Sydney CBD.
[You may assume that the unknown population standard deviations for Parramatta and Sydney businesses are equal]
QUESTION 6 (5 marks)
Test, at the 5% level of significance, whether location (Parramatta or Sydney CBD) of the business is related to type of business (privately held, publicly traded or franchise)?
NOTE: The data for Part 2 was randomly created for the sole purpose of this assignment. The data for Part 2 can be assumed to be normally distributed for all continuous variables Questions are attached below