a. An economist uses the price of a litre of orange juice as a measure of inflation. She nds that the average price is RM 7.00 per litre and the population standard deviation is 111510.66. You decide to sample 80 small shops, collect their prices for a litre of orange juice, and compute the mean price for the sample. i. ii. What assumptions do you need to make about the shape of the population distribution of all possible price of a litre of orange iuice to make inferences about the average price of orange juice? (2 Mark) What are the expected value, standard deviation, and shape of the sampling distribution of the sample means? (3 Marks) What is the likelihood that the sample mean is between RM 6.92 and RM 106? (3 Marks) b. Below is the sample of ve lecturer's hours of teaching at a community college. is: ID 5 15 10 20 Construct a 95 percent condence interval estimate for the population mean amount of teaching hours. What assumption you must make before you proceed with the calculation? justify your answer. (9 Marks} Interpret the interval constructed in h) above. (2 Marks} The teachers who teach less than 16 hours are considered as researchers. Let's assume that in a new ample of teachers at the same community college, there are; a} Five teachers teaching for 10 hours, b} Fifteen teachers teaching for 5 hours. c) Fifteen teachers teaching for 15 hours cl} Five teachers teaching for 20 hours. Using the information in b(ii1')(a)-b(1ii}(d) above, construct a 95 percent confidence interval estimate for the population proportion of teachers who teach less than 16 hours. Interpret your answer. (11 Marita)