1. The following table shows the sample correlations between, the monthly returns for four different mutual funds and the S&P 500. The correlations are based on 36 monthly observations. The funds res followed. Fund 1 Large-cap fund Fund 2 Mid-cap fund Fund 3 Large-cap value fund Fund 4 Emerging markets fund Fund 1 Fund 2 Fund 3 Fund 4 S&P 500 Fund 1 Fund 2 0.9231 Fund 3 0.4771 0.4156 Fund 4 0.7111 0.7238 0.3102 S&P 500 0.8277 0.8223 0.5791 0.7515 Test the null hypothesis that each of these correlations, individually, is equal to zero against the alternative hypothesis that it is not equal to zero. Use a 5 percent significance level. 2. Bouvier Co. is a Canadian company that sells forestry products to several Pacific Rim customers. Bouvier's sales are very sensitive to exchange rates. The following table shows recent annual sales (in millions of Canadian dollars) and the average exchange rate for the year (expressed as the units of foreign currency needed to buy one Canadian dollar). Year i Exchange Rate X; Sales Y. 0.40 20 0.36 25 0.42 16 0.31 30 in 0.33 35 0.34 30 3. Calculate the sample mean and standard deviation for X and Y b. Calculate the sample covariance between the exchange rte and sales c. Calculate the sample correlation between the exchange rate and sales Calculate the intercept and coefficient for an estimated linear regression with the exchange rate as the independent variable and sales as the dependent variable. 3. Julie Moon is an energy analyst examining electricity, oil, and natural gas consumption in different regions over different seasons. She ran a regression explaining the variation in energy