A scientist went through the forest and measured the weight of moss found at the base of a tree, and the length of a leaf from that tree. The sample size n = 20 trees, the correlation coefficient r = 0.55, and the rest of the data is summarized in the table below. X = weight of moss in grams Y = length of leaf in inches mean 5.00 2.50 standard deviation 0.25 0.20 a. (2 pts) Calculate (or bound) the p-value to test the null hypothesis that x and y are uncorrelated. b. (2 pts) Repeat part (a) if everything is the same except now the sample size n = 40. c. (2 pts) Calculate the slope b1 and intercept b0 of the least squares line. d. (2 pts) Define residual. What assumptions does the linear model make about residuals? e. (2 pts) Calculate the approximate residual standard deviation se. (9. continued) For problems (f) and (g) transform the y units from inches to cm (1 inch = 2.54 cm). f. (2 pts) How does the value of the correlation coefficient r change? g. (2 pts) How does the value of the residual standard deviation se change? h. (2 pts) Does this data show that heavy clumps of moss at the base of a tree cause tree leaves to grow longer? Explain why or why not.

X = weight of moss in grams Y = length of leaf in inches

mean 5.00 2.50

standard deviation 0.25 0.20