lmputation: The le interexp . dat contains data from an experiment that was interrupted before all the data could be gathered. Of interest was the difference in reaction times of experimental subjects when they were given stimulus A versus stimulus B. Each subject is tested under one of the two stimuli on their rst day of participation in the study, and is tested under the other stimulus at some later date. Unfortunately the experiment was interrupted before it was nished, leaving the researchers with 26 subjects with both A and B responses= 15 subjects with only A responses and 17 subjects with only B responses a] Calculate empirical estimates of 9,4? 6'3? p: 03, 025 from the data using the commands mean , our and var . Use all the A responses to get m and 13:4? and use all the B responses to get $3 and 6%. Use only the complete data cases to get ,5. b] For each person 1' with only an A response, impute a B response as es = 5's + (\"yea '9.4l15'1|3 Garza/\".24- For each person 1' with only a B response, impute an A response as Eli-4 = 9.4 + [yes - gel-'fgf. You now have two \"observations" for each individual. Do a paired sample ttest and obtain a 95% condence interval for SA 195. c] Using either Jereys' prior or a unit information prior distribution for the parameters, implement a Gibbs sampler that approximates the joint distribution of the parameters and the missing data. Compute a posterior mean for SA 6'3 as well as a 95% posterior condence interval for SA :93. Compare these results with the results from b) and discuss.|