The data file sp500stocks. cev measures several variables on n = 505 companies that make up the SAP 500 Index. Use this data set for both problems 2 and 3. The variables in the data set include: ticker: a unique identifier of the company for stock exchanges Category: whether a Common stocks or Real Estate Investment Trusts (REITs) type cap: whether a Mid cap or Large cap stock sector: which of 11 sectors the company mainly resides marketcap: market capitalization, in billions plearn: price to earnings p2sale: price to sales p2book: price to sales divyield: dividend yield return: year-to date return: percentage change in stock price from Jan 1 to Oct 15 (a) Visually explore and numerically summarize the distribution of return. Comment on what you notice and describe the distribution. You and your friend have an argument as to what the best sector of large stocks is the best for investing in during the pandemic: your friend says it's the Financials sector while you believe it's the Health Care sector (due to the influence of the pandemic). You decide to investigate these claims based on the companies in the SAP 500 which are listed in the sp500stocks.cav file. The useful variables in this data set include sector (which sector the company is in) and return (the past yearly return: change in percentage points). (b) Perform an appropriate formal hypothesis test to determine whether you or your friend is correct based on the returns of the associated stocks in the S&P 500. Be sure to include all the steps of a hypothesis test. (c) In actuality, your friend really had no idea which sector should be best, so they took a peak at the data set before choosing the Financials sector based on what the data suggest. Comment on the validity of the test results from part (a) and why the results may be misleading (d) Provide a visual and fit a linear model (modell) to determine whether return varied across sectors on average, and include the summary output of the model. Based on this model: which sector performed best? Which sector performed worst? (e) Perform an appropriate hypothesis test to determine whether return is significantly associated sector in modell. Comment on the assumptions to this test. (f) Perform an appropriate hypothesis test using modell to determine whether stocks in the Financials sector perform differently from stocks in the Health Care sector. (g) Compare your results from part (f) and part (b) above. Conceptually explain why the results of the calculations are the same or different