8. Two independent stations were chosen for a study. For 6 monthly samples collected at the first station, the species diversity index had a mean value 21 = 2.14 and a standard deviation $1 = 0.371, while the 12 monthly samples collected at the other station had a mean index value of 12 = 3.24 and a standard deviation $2 = 0.228. Find a 63% confidence interval for the difference between the population means of the diversity index at the two locations, assuming that the two populations are approximately normally dis- tributed with equal variances. Show work, show the appropriate formulas, use proper notation, and show how you plug numbers into formulas. (Use R here only to find the appropriate critical value.) (11 points)