Exercise 7

QUEEN MARY, UNIVERSITY OF LONDON MTH6991/MTH791U/MTH791P Computational Statistics with R Exercise Sheet 7

Spring 2019

Please submit your solution only for the designated problem(s), but try the other problems for practice. There will be a link on QMPlus to submit the solution. The deadline is 2pm on Friday the 15th March. Late submissions will not be accepted.

Submit a file containing the R code used, but report the results in your own words - you don’t need to include any R output. Submit the R code either in a text file (.txt) or an R script (.R). This file can also contain the solutions to the questions, or you can use a Word document or pdf file for these. 1. (Problem for handing in, 30 marks) This question uses the same dataset as exercise sheets 5 and 6, of test marks for each student in a class before and after some extra teaching sessions. Calculate a 95% confidence interval for the difference between the “before” and “after” scores using the BCa bootstrap method. What does the confidence interval tell you about the test scores? 2. (Problem for handing in, 70 marks) This question uses the dataset from exercise sheet 4. This dataset has two columns, named “control” and “treatment”, which are the blood pressure measurements in a clinical trial. These measurements are two independent samples, not measurements on the same individuals. Calculate the bootstrap standard error and a 95% percentile confidence interval for the difference between the means of the measurements for the two groups. Suppose that we are interested in how the variability of the two groups compares, as measured by σC r= σT where σC and σT are the standard deviations of the measurements in the control and treatment groups, respectively. Calculate a 95% bootstrap confidence interval for r.

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3. Consider the law dataset that we looked at in practicals 7 and 8. We wish to find a 95% BCa confidence interval for the correlation between the two scores, LSAT and GPA. Do the following in R, but without using the