ASSIGNMENT 2 Due I'lprrl Thursday, September 15 Total Marks: 41] This assignment covers material in chapters 5-9 of the Unit Notes. R is not required in this as signrnent, but may be used if you wish. If software is used, attach relevant output to support your answers. No data files are required. 1. [It] marks] An automated bloodvpressure machine classies people as having either high blood pressure {hypertension} or normal {healthy} blood pressure. In clinical trials on adults the mav chine classified 839-1: of hypertensives as having hypertension, and classied 229-1: of healthyr peo- ple, i.e. without hypertension, as having hypertension. Health ofcials are considering using the machine for screening an adult population in which 1859:: of persons have hypertension. {a} Structure the above information using a contingency table. Take care to complete all marginal totals as well as the body of the table. [4] [b] Estimate the proportion of people that the machine classifies as hypertensive that would actually have hypertension? [2] [c] Consider those who would be classified by the machine as having normal blood pressure. If we chose one of these people at random, what is the chance that the selected person would actually be hypertensive? [2] [d] What would the machine do better in this population: show who has hypertension, or show who doesn't have it? Justify your answer. [2] 2. [12 marks] In Australia, Silt-b of the population has blood type at\". Consider X, the number having .4 + blood among 18 randomly-selected Australians. {a} What is the probability distribution of X? [3] [b] Calculate: {i} the mean and standard deviation of X. [3] iii} Pix :1? 12} [2] {iii} P{:'r-=_: X '2: ID} [2] [c] If, in such. a sample, you found only 5 people with. A' blood, would this be an unusual sample? lustify your answer using an appropriate probability calculation. [2] 3-. [3- marks] Suppose the random variable, \"1", has the probability distribution, {a} Calculate the mean, and [l] [b] the standard deviation [2]