Question 1 The following (artificial) data record the length of stay (in days) spent on a psychiatric ward for 28 consecutive patients who have been sectioned under the mental health act, classified...

Question 1 The following (artificial) data record the length of stay (in days) spent on a psychiatric ward for 28 consecutive patients who have been sectioned under the mental health act, classified according to their gender: Male: 96 113 195 22 56 155 30 50 29 38 25 79 34  Female: 39 71 17 9 35 6 57 10 18 65 35 21 32 28 16 Estimate the median length of stay, giving an approximate 95% confidence interval, for males and females separately. Carry out a test to determine if there is a significant difference between males and females with regards to the median time spent on a psychiatric ward after being sectioned. Estimate the probability that a randomly chosen male patient will stay longer than a randomly chosen female patient. Question 2 General trace organic monitoring describes the process in which engineers analyse water samples for various organic materials (e.g. contaminants). The data below record the total organic carbon concentration, X, in 13 water samples collected from a river: X: 5.1 5.7 7.5 8.1 5.8 6.1 3.1 7.1 9.2 3.7 4.4 6.8 9.8 Estimating the sample Cumulative Distribution Function (CDF) by S(xi) = i/(n + 1), use the Kolmogorov-Smirnov test to examine if these data are consistent with coming from a Normal distribution having mean 7.0 and standard deviation 2.0.Obtain the Normal Equivalent Deviates corresponding to the observed values of X and use these to produce a Q-Q plot. Does your plot indicate that these data are consistent with coming from a Normal distribution? Question 3 An article "Does it pay to plead guilty? Differential Sentencing and the Functioning of Criminal Courts" [Law and Society Review, 1981] considered the punishments metered out to 255 individuals found guilty of robbery. All individuals had previous convictions. Of the 191 who pleaded...