Question 16 (11 marks) [6 + 2 + 3 = 11 marks] In Australia, there is a distinction between plastic surgeons and cosmetic surgeons. Plastic sur- geons are regulated (they require at least 12 years of training, and membership of a professional body) whereas cosmetic surgeons are not (only requiring a basic 4 year medical degree). De- spite the differences, most Australians use the terms "plastic surgery" and "cosmetic surgery" interchangeably. Page ly (a) A small random survey found that 23 of the 25 people surveyed agreed with the statement "A plastic surgeon and a cosmetic surgeon are the same." Use the Minitab output to conduct a hypothesis test to determine if the proportion differs from 0.5. You should state your hypotheses, calculate an appropriate test statistic, give a range for the P- value, and state your conclusion in the context of the survey. Normal with mean = 0 and standard deviation = 1 P( X S X ) 0.800 0.84162 0.900 1.28155 0.950 1.64485 0.975 1.95996 0.990 2.32635 0.995 2.57583 0.999 3.09023 19 of 27 - add any extra pages after page 27(b) In part (a) you have used a test based on an approximation. Was this appropriate? (c) A larger survey is being planned, and the desired margin of error for a 95% confidence interval is 0.05. Assuming that the proportion who agree with this statement is not smaller than 80%, how large a sample is required