An education authority provides children with musical instrument tuition. The authority is concerned about the number of children giving up playing their instrument and is testing a new tuition method with a proportion of the children which it hopes will improve persistency rates. Data have been collected and a Cox proportional hazards model has been fitted for the hazard of giving up playing the instrument. Symmetric- 95% confidence intervals (based upon standard errors) for the regression parameters are shown below. Covariate Instrument Confidence Interval Piano Violin Trumpet Tuition method Sex Traditional New Male Female 0 [-0.05,0.19] [0.07,0.21] 0 [-0.15,0.05] [-0.08,0.12] 0 (i) Write down a general expression for the Cox proportional hazards model, defining all terms that you use. (ii) State the regression parameters for the fitted model. [3] [2] (iii) Describe the class of children to which the baseline hazard applies. [1] (iv) Discuss the suggestion that the new tuition method has improved the chances of children continuing to play their instrument. [3] (v) Calculate, using the results from the model, the probability that a boy will still be playing the piano after 4 years if provided with the new tuition method, given that the probability that a girl will still be playing the trumpet after 4 years following the traditional method is 0.7. [3] [Total 12]