Question 28 Smoking is a huge societai issue. A sample of 35 young people was taken to investigate e- cigarette/vaporing smoking behaviour. a) '3) According to the sample on average 7.6% of people between 15- 17 years old have used an e-cigarette or vaping device, with a standard deviation of 2.7. Construct a 98% confidence interval for the true proportion of ecigarette smokers between 15-17 years of age. [7 marks] The same sample found that on average young people smoked 8 hours a week, with a standard deviation of 1.5 hours a week. Construct 95% confidence interval for the true mean of times young people smoke ecigarette a week. [7 marks] Based on the information obtained above in question b) but knowing that the population standard deviation is 2.05 hours a week, construct 98% condence interval for the true mean of times young people smoke ecigarette a week. [6 marks] [Total for Question 28 = 20 marks] Question 29 A market researcher wants to study weekly individual income in a specic suburb of Northern Tasmania. a) If she can tolerate an error of $200 with a probability of 98%, and it is known that q = $593, what is the optimal sample size? [7 marks] b) Based on a sample of 40 people, the mean weekly income is $1,090 with a sample standard deviation of $310, test at the 1% signicance level that the sample is from a population with u = $1,100. [6 marks] c) Based on another sampie of 75 people, the sample mean weekly income is $1,078. If it is known that the population standard deviation is $270, test at the 5% signicance level that the weekly average individual income for the population is lower than $1,000. [7 marks] [Total for Question 29 = 20 marks]