Question 3 [20 marks] a) Dr. Susan is an industrial psychologist. She is currently studying stress among executives of internet companies. She has developed a questionnaire that she believes measure stress. A score above 80 indicates stress at a dangerous level. A random sample of 15 executives reveals the following stress level scores: 94 78 83 90 78 99 97 90 97 90 93 94 100 75 84 i. Use your calculator or otherwise, find the mean and standard deviation of the stress level for this sample. What is the best point estimate of the population mean? [3 marks] ii. Construct a 95% confidence level for the population mean. Assume that the population distribution is normal. [5 marks] iii. According to Dr. Susan test, is it reasonable to conclude that the mean stress level of internet executives is 80? Justify your answer. [2 marks] b) Dr. Susan conducted another survey and the result shows that out of 270 executives, 46 have stress score above 80 i. Develop a 95% confidence interval for the proportion of executives who have stress score above 80. [5 marks] ii. Is it possible that the population proportion is 18%? [2 marks] iii. What sample size is needed to estimate the proportion within 0.5% and a level of confidence of 95%? [3 marks]