Question

Problem 2 – Lockyer Valley housing price

To test if this belief is correct, a random sample of 86 properties is selected. The mean of the valued housing price computed from the sample is $510,000. Assume that the population standard deviation of the housing price in the region

is $50,000.

Lockyer Valley is located in the West Moreton region of South East Queensland. It has

a population of 41,011 people. A real estate office claims that the average housing price in

Lockyer Valley is more than $500,000.

a) Assist the office in performing a hypothesis test at a 5% level of significance to check whether the claim made is justified. Display the six steps process (involving drawing the rejection region/s and determining the critical value/s for the decision rule) in performing the test. 6 marks

b) Calculate the p-value of the test above. Display working. State the decision rule of the test should you want to use the p-value method hypothesis testing. 2 marks

c) This hypothesis test is conducted on the basis that the sampling distribution of the sample mean is approximately normally distributed. Specify the required condition to ensure this. 1 mark

d) Identify which one of these two types of error (Type I or Type II) you could make when drawing the conclusion in part a). Briefly explain your selection. 1 mark

Answer 1