6. Below are the yearly precipitation totals (x), in inches, paired with annual lowest lake levels (in feet down from a full lake) (y) at Big Bear Lake, in California, for a collection of randomly selected years. Test the claim at 6% significance that the population of (x, y) pairs exhibits linear correlation. (Data from the Big Bear Municipal Water District). X 15.02 30.62 24.82 50.40 27.00 41.04 49.00 31.78 17.32 y 13.98 9.89 7.38 1.22 5.67 4.57 2.48 3.78 12.17 (a) For the problem given, calculate the test statistic and the p-value. (6 points each) (b) The conclusion is that we should reject the null hypothesis. (6 points) Write the very short conclusion sentence that explains the result in context. (c) Write the regression model for this problem. Use correct notation. (6 points) (d) Use the regression model to predict the lowest lake level during a year where the yearly precipitation level is 45 inches. Show all calculations, write a sentence that explains the prediction in context. calculations (6 points) context sentence (7 points) (e) Use your calculator to build a 92% confidence interval for the slope of the regression line for this data set. No work required. Use correct notation. (8 points)