QUESTIONS Q1. [3 Marks] Realestate.com.au reports that the median property price in Randwick in September 2021 was $3,080,000 (https:[[www.realestate.com.auzneighbourhoodszrandwick-2031-nsw). Suppose that the mean price was $4,000,000 and the standard deviation was $200,000. a. If you take samples of size n=2, describe the sampling distribution of)? Does this change if you take samples of size n=100? If so, describe the shape of the sampling distribution of X. (1 mark) b. If you take a random sample of size n=100, what is the probability that the sample mean will be less than $3,800,000? (2 marks) Q2. [3 Marks] a. If)? = 125, a = 24, and n = 36, construct a 99% confidence interval estimate of the population mean u. (1 mark) h. In deciding what salaries to pay new recruits with Honours degrees in economics, a company reviews data on industry salary rates. The person responsible for the analysis says that she has 95% confidence that salaries are between $120,000 and $150,000. Explain the meaning of this statement. (2 marks) Q3. [4 Marks] A company that makes canned soup is being audited by an industry regulator to make sure that the amount of soup in each 400 gram can of soup is in fact 400 grams. They inform the regulator that the population standard deviation for 400-gram cans is 5 grams. A random sample of 100 cans indicates a sample mean of 399 grams. a. Construct a 95% confidence interval estimate of the population mean amount of soup in each can. (1 mark) b. Must you assume that the population of the amount of the soup in the cans is normally distributed? Explain. (1 mark) c. Explain why a value of 404 grams for a single can is possible, even if it may be outside the confidence interval you calculated. (1 mark) d. Suppose that the sample mean had been 401 grams. What is your answer to (a) with this new sample mean? Has the width of the confidence interval changed? (1 mark)