Manconi et al XXXXXXXXXXinvestigated the objective-subjective mismatch in sleep perception. In one part of the study, the total sleep time mismatch (T STobjective − T STsubjective) was measured for a sample of 159 self-diagnosed insomniacs and a sample of 288 normal sleepers (controls). (T STsubjective is the total time (minutes) that the individual estimated they slept (upon wakening), and T STobjective 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 file 2040_W22_sleep_insomnia_both.csv
a) Plot side-by-side box plots of the data (in one plot). Label the plot appropriately. Plot normal quantile-quantile plots for the two groups separately. Include the plots in your submission.
) 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.
c) Choose to analyze the data with either the pooled-variance t or Welch’s t procedure. Justify your choice.
d) Give the R output for your choice of procedure.
e) Interpret the results, including commenting on the results of the test of the null hypothesis that the true mean mismatch time is the same for both groups, and an appropriate interpretation of a relevant confidence interval. Interpretations must relate to the problem at hand.
f) If we wish to use information in this study to draw conclusions about self-diagnosed insomniacs vs normal sleepers in general, what biases might be present? (You’ll need to look at relevant bits of the journal article to answer this.)