Stat 311 Homework 5 5. Recall the popular diets data set (PopularDiets.csv) that we have used before. We created a new data set called PopularDietsCombined.csv. It only contains observations for participants that completed the study, and it only contains the two variables WTLossKG (weight loss in kilograms) and Diet. 8) b) g) h) .i) k) Read in the data and make a quick boxplot to refresh your memory that there did not seem to be much difference in weight loss by diet. We provide the read statement in HomeworkS Template.and. Use the boxplot function in base R to get a quick comparative boxplot of weight loss by diet. No need to write anything here- Since there does not seem to be too much difference by diet type, we will only work WTLossKG. What is the point estimate for mean weight loss across all diets? Using all 93 observations across all diets, create 1000 bootstrapped samples. Display a histogram of the bootstrapped distribution for mean weight loss. Set the number of bins to 10 if you use ggplotz for the histogram. Describe the shape of the distribution. What do we mean by the \"bootstrap distribution\" for weight loss? Explain. Report the 95% bootstrap condence interval for mean weight loss and provide an interpretation of this interval in the context of the problem. Use set . seed (10) . Report the 90% and 99% bootstrap condence intervals for mean weight loss from the same bootstrap sample. How do these intervals compare with the 95% interval reported in part (e)? If you redraw your bootstrap samples, use set . seed (10) before each set of draws. If you were to draw a new set of 1000 bootstrap samples and find the 95% bootstrap condence interval, how do you think the new interval will compare with the interval reported in part (e)? Answer this before doing part (h) below. This question is effort only. Draw two new sets of 1000 bootstrap samples using the 93 observations and report the 95% bootstrap condence interval for mean weight loss for each (no need to plot the two new bootstrap distributions and do NOT use set . seed). Do these intervals support what you wrote for part (g)? Explain. If you drew smaller sized bootstrap samples (fewer than 1000 reps) and calculated the 95% bootstrap condence interval, how do you think the new intervals would compare with the interval reported in part (c)? Answer this before doing part (j) below. This question is effort only. Use set . seed (10) and draw bootstrap samples using n = 500, 100, and 10 reps (be sure to reset the seed before each new rep size). Report the 95% bootstrap confidence intervals for mean weight loss for each of these new sets. Do these intervals support what you wrote for part (i)? Explain. Now make two subsets of the data, one for the Ornish diet and one for the Weight Watchers diet. Use set . seed (10) and draw 1000 bootstrap samples to report a 95% bootstrap condence interval for mean weight loss for each diet (so two CIs). Be sure to reset set. seed (10) for each diet type. Compare the intervals. What can you say about mean weight loss for the Ornish diet compared with the Weight Watchers diet based on the two condence intervals