A student is assessing the correlation between the number of hours a plant receives sunlight and the height to which it grows. The table below shows the data: Number of hours of sunlight (x) 0 1 2 3 4 5 6 7 8 9 Height of plant in cm (y) 4 7 10 13 16 19 22 25 28 31 Part A: Is there any correlation between the number of hours of sunlight that a plant receives and the height to which it grows? Justify your answer. (4 points) Part B: Write a function which best fits the data. (3 points) Part C: What does the slope and y-intercept of the plot indicate about the plant? (3 points) (10 points)

Farmers know that driving heavy equipment on wet soil compresses the soil and injures future crops. here are data on the "penetrability" of the same type of soil at two levels of compression. penetrability is a measure of how much resistance plant roots will meet when they try to grow through the soil. compressed soil 2.85 2.66 3 2.82 2.76 2.81 2.78 3.08 2.94 2.86 3.08 2.82 2.78 2.98 3.00 2.78 2.96 2.90 3.18 3.16 intermediate soil 3.17 3.37 3.1 3.40 3.38 3.14 3.18 3.26 2.96 3.02 3.54 3.36 3.18 3.12 3.86 2.92 3.46 3.44 3.62 4.26 use the data, omitting the high outlier, to give a 95% confidence interval for the decrease in penetrability of compressed soil relative to intermediate soil. compute degrees of freedom using the conservative method. interval: to