I think about a two-sample t-test for independent populations as a special case of an ANOVA where the number of groups is just 2. Given this way of viewing things, you might wonder if we will get the same results pushing data through a two-sample t-test vs. an ANOVA with two groups. Let's find out. Using R, read in the file pi. csv which has 10000 digits of = 3.1415926 We'll compare the digits in the odd indices (3, 4, 5, 2, etc.) with those in the even indices (1, 1, 9, 6, etc.). a. Write code that compares the average digit in odd and even indices using a t-test. Give your t-stat and P-value. (PHNTOM, code] b. Repeat your analysis using an ANOVA. You'll need to figure out how to build a data frame formatted for an ANOVA. Include your F-stat and P-value. (PUNTOM, code] c. What relationship exists between the t-stat and F-stat? Between the P-values? d. The relationship between the t-stat and F-stat suggested by part c is actually the consequence of a relationship between the distributions T. and F By playing around with code in R, find a relationship between these distributions. Include the code that led to your conjecture relating these two distributions. Again, this is a problem where a Google search immediately gives the answer. Resist this temptation; learning is about the journey, not just the destination