Problem 2 - Used car price evaluation(10 marks)

It is estimated that around 13% of the residents of Jakarta use cars to commute.Despite the current Covid-19 pandemic, a large car dealership in the city reported that the demand for used mid-size passenger sedans in the city has become stronger.The dealership further claimed that the average selling price for used mid-size passenger sedans is now more than $9,500.In verifying this, a random sample of 120 used mid-size passenger sedans is selected.The average price calculated from the sample is $9,600.Assume that the population standard deviation of the price is $1,200.

a)Suppose you were a junior business analyst working for the dealership.Assist the dealership in performing a hypothesis test at a 10% level of significance to check whether the dealership's claim is supported.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)Specify the decision rule to use in the p-value method hypothesis testing. Calculate the p-value of the test above.Display working.2 marks

c)Which one of these two types of error (i.e Type I or Type II) you could make with the conclusion you made in part a)?Briefly explain your selection. 1 mark

d)What is the required condition for ensuring that the sampling distribution of the sample mean is approximately normally distributed?Check if the condition is satisfied in the hypothesis testing that you just completed.1 mark