Question 1 (10 marks) In this question we will revisit our analysis of the COVID-19 recovery data that we began in Assig

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Question 1 10 Marks In This Question We Will Revisit Our Analysis Of The Covid 19 Recovery Data That We Began In Assig 1 (390.06 KiB) Viewed 123 times

Question 1 10 Marks In This Question We Will Revisit Our Analysis Of The Covid 19 Recovery Data That We Began In Assig 2 (18.45 KiB) Viewed 123 times

Question 1 (10 marks) In this question we will revisit our analysis of the COVID-19 recovery data that we began in Assignment 1. The file covid. 19. ass2.csv contains a subset of the New South Wales days-to-recovery data we examined previously; this time, patients with recovery times over four weeks (28 days) were removed as these recovery times are unusual and likely represent a sub-population of people more susceptible to the virus. We know from Assignment 1 that the Poisson distribution is not a good fit to the recovery data: instead, for this question we will use a normal distribution as it provides an improved fit to the data due to its increased flexibility, while accepting this assumption is also not necessarily correct; to quote the famous statistician G.E.P.Box: “all models are wrong - but some are more useful than others". Important: you may use R to determine the means and variances of the data, as required, and the R functions qt() and pnorm() but you must perform all the remaining steps by hand. Please provide appropriate R code fragments and all working out. 1. Calculate an estimate of the average number of days to recovery using the provided data. Calcu- late a 95% confidence interval for this estimate using the t-distribution, and summarise/describe your results appropriately. Show working as required. [4 marks] 2. Similar data was collected in 2020 by the Israeli Ministry of Health. While the specific data was not available, the summary statistics were provided, and from these I have simulated a dataset of n = 494 individuals from the Israeli study. The days to recovery in this group are provided in the file israeli.covid. 19.ass2.csv. Using the provided data and the approximate method for difference in means with different) unknown variances presented in Lecture 4, calculate the estimated mean difference in recovery times between the Israeli patients and the patients from NSW, and provide an approximate 95% confidence interval. Summarise/describe your results appropriately. Show working as required. [3 marks] 3. It is of interest to determine if there are any differences, at a population level, in recovery times for patients in different countries. Test the hypothesis that the population average time taken to recover for the Israeli cohort is the same as in the NSW cohort. Write down explicitly the hypothesis you are testing, and then calculate a p-value using the approximate hypothesis test for differences in means with (different) unknown variances presented in Lecture 5. What does this p-value suggest about the difference in mean recovery time between the two cohorts of patients? [3 marks]
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