ECON7300 Statistics for Business and Economics- final exam

Question 1 [5 marks]

Medical researchers have discovered that 75% of people who have suffered a heart attack had periodontitis. Only 30% of healthy people (i.e., those not suffering a heart attack) have periodontitis. Suppose that in a certain community, heart attacks are quite rare, occurring with only 5% probability. If someone has periodontitis, what is the probability that he/she will not have a heart attack?

Question 2 [4 marks]

ABC TV network decides to cancel one of its shows if it is convinced that less than 15% of the viewing public are watching this show. If a random sample of 2000 households with television is selected, what sample proportion values will lead to this show's cancellation? Assume a 5% significant level.

Question 3 [5 marks]

Suppose an autoregressive model is used for data in which quarterly sales in 2018 were: $1800 (in quarter 1), $1200 (in quarter 2), $2800 (in quarter 3), and $3400 (in quarter 4). Using these data, a first-order autoregressive model is fitted and has the following estimated parameters: a0 = 0.15 and a1 = 1.25

Based on this information, compute the forecast for (a) quarter 4 of 2019. (3 marks)
(b) quarter 4 of 2020. (2 marks)