c) Suppose we decide to use the t procedures to analyze the data. Use t.test in R. to calculate a 95% condence interval for the population mean percentage. Include the output from R in your submission. d} Give an appropriate interpretation of the 95% condence interval given by R, in the context of the problem. e) Carry out a test of the more meaningful test: H0: p. = 0 or HD: ,u = 10. Justify your choice of hypothesis. (Recall that choice of hypothesis has nothing to do with the data in the current sample, or default output from software, but is based on the nature of the problem at hand.) Give the hypotheses in words and symbols, get the appropriate if statistic and pvalue from the R output, and give an appropriate conclusion to this test. Your submission must include the boxplot, the normal QQ plot, and the R. output, in addition to your comments and interpretation. Your submission for this part should only be two pages, but can be three pages if you feel that is necessary. 2 Subjective and objective sleep time mismatch in insomniacs and normal sleepers (30 marks total) Consider again this information from Assignment #1. Manconi et al. (2010) investigated the objectivesubjective mismatch in sleep perception. In one part of the study, the total sleep time mismatch (TSTobjectme TSEubjem-m) was measured for a sample of 159 self-diagnosed insomniacs and a sample of 288 normal sleepers [controls]. [TSTsubjediw is the total time (minutes) that the individual estimated they slept (upon wakening), and TSTobjectwe is the total time they slept as measured by technology. The difference is the mismatch, and these mismatch times are given in the data set. Positive mismatch times indicate the individual thought they slept for less time than they did.) The data is contained in the le 2040_W22_sleep_insomnia_both.csv. Is there evidence of a difference in mismatch times for normal sleepers and self-diagnosed insomniacs? You must import this data set into R to carry out the analysis. You will need to use an appropriate 1: .test command to carry out the calculations. For your write-up to be complete, you must: a) Plot side-by-side box plots of the data (in one plot). Label the plot appropriately. Plot normal quantilequantile plots for the two groups separately. Include the plots in your submission. b} Comment on the whether the normality assumption of the two-sample t procedures is reasonable in this setting. You should make reference to the plots. If you feel there is a violation of the normality assumption, do you think it is still reasonable to use the t procedure here? Justify your position