Question

Question 3

Warwick is a suburb in the Southern Downs Region of Queensland. Warwick has a population of 12,223 people and 32.29% of its occupants live in rental accommodation. A real estate office claims that the average rental price in Warwick is less than $400 per week. To test if this belief is correct, a random sample of 96 rental properties is selected. The mean of the weekly rental price computed from the sample is $385. Assume that the population standard deviation of weekly rental price is $100.

a) You were recently hired as a junior data analyst working for the real estate office. Assist the office in performing a hypothesis test at a 3% 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.

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.

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.

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.

Answer 1