1. [12 marks] Historical \"experience\" suggests that if a drug to treat high blood pressure is given under medical supervision to 4 randomly selected, previously untreated, patients with high blood pressure, the number of patients for whom it is brought under control follows the distribution: Brought under control 0 1 2 3 4 Proportion 0.009 0.075 0.260 0.416 0.240 The company supplied the drug to 130 doctors who agreed to use it on their next 4 patients. For 24 of the doctors, the treatment was successful with all 4 patients, for 59 it was successful with 3, 33 with just 2, and 14 with only 1 of the next 4 patients. Are these results consistent with the distribution of successes expected by the company? Evaluate with a suitable hypothesis test at 5% signicance level, taking care to evaluate and address any concerns over the assumptions. 2. [13 marks] Statins are widely prescribed to treat high cholestorol. However, they are known to have some unfortunate side-effects. One study advertised for volunteers aged 30 50 years who were ei- ther currently taking statins under medical supervision, or not taking statins at all. A small fee was offered to accepted participants, and evidence of identity was required (e.g., driver '5 licence). Volunteers were screened to ensure that none had the same address, or belonged to the same family, and no more than 5 shared the same postcode. No applications were accepted from addresses that lay outside Australia or appeared to be aliases. After screening, accepted participants were asked to maintain a daily diary for a week via an online form that asked about a range of possible side-effects. Confirmation of statin dosage (if any) was obtained from their doctor. The table below summarises participants' journal entries regarding back pain, classied by statin dose. No Back Pain Test the hypothesis that, among Australians aged 30 50 years, occurrence of back pain is un related to statin dose. Include discussion of assumptions and take appropriate action regarding any problems. If you conclude that there is a relationship, describe it. Use a 5% signicance level. You may assume that the checks on identity and location are adequate