Stock Volatility: Investors will commonly discuss volatility in stocks, which is closely related to the variance in the stock return, or price. Using the Weekly data, let$$s explore whether returns in year $2008,$ the year that $$The Great Recession$$ began, contained greater volatility than in returns in year $2005,$ a year where the stock market was still on a relatively climb up to the peak reached in late $2007.$

a$)$ What needs to be done to accomplish our goal?

b$)$ Create a filtered dataset from Weekly that contains only information we are interested in$.$

c$)$ Using the filtered dataset, create visualizations summarizing of the distribution of the difference in volatility $($variance$)$ between the two years in this data. The quantity of interest is a Random Variable and would be written s$22005$ s$22008$ in mathematical terms. It may be helpful to create two datasets, Weekly$2008,$ and Weekly$2005,$ which contain only weekly returns from the specified years, and then

sample with replacement within each of these datasets manytimes $($think bootstrapping$)$ in order to create a sample of differences in variance $($volatility$).$

d$)$ Estimate the standard error of the difference in volatility $($variance$)$ between years $2005$ and $2008$ in the Weekly data. This would be written s$22005$ s$22008$ in mathematical terms.

e$)$ Provide some evidence for or against the argument that $2008$ was a more volatile year than $2005.$ Make sure to use resampling or statistical methods to make this argument. Your answer should be in the form of a confidence interval