The daily stock returns of stocks are independent and identically distributed process. Over 2 month (= 40 trading days), it is observed that the average daily returns of a randomly picked stock is 2%; and the standard deviation of the daily returns is 4%. An analyst wants to test the null hypothesis of underlying or population mean daily returns equal to 1%. What are the corresponding test statistic and the degree of freedom for the test? Over the same 40 trading days, the analyst analyzed another stocks daily returns and calculated its correlation with the daily returns of the 1st stock as 0.40. The analyst wants to test the null hypothesis of no correlation between the daily returns of the 2 stocks. What are the corresponding test statistic and the degree of freedom for the test?