Country : Australia
Assignment Task:

Question 1

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 

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 

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) 

Question 3

Calculate a 95% confidence interval for the unknown population mean business age. 

Question 4 

Test, at the 1% level of significance, whether the average business has more than 15 employees. 

Question 5

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

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)? 

 

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  • Posted on : May 25th, 2019
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