6. The following table presents interest rates, in percent, for 30-year and 15-year fixed rate mortgages, for January through December, 2012. [4 pts] 30-Year 15-Year 30-Year 15-Year 3.92 3.20 3.55 2.85 3.89 3.16 3.60 2.86 3.95 3.20 3.47 2.78 3.91 3.14 3.38 2.69 3.80 3.03 3.35 2.66 3.68 2.95 3.35 2.66 (a) Construct a scatterplot of the 15-year rate (y) versus the 30-year rate (x) (b) Compute the correlation coefficient between 30-year and 15-year rates. If you use your calculator to obtain a "fast" result, write down the calculator steps you used to obtain your answer. (c) When the 30-year rate is below average, would you expect the 15-year rate to be above or below average? Explain. (d) Which of the following is the best interpretation of the correlation coefficient? When a bank increases the 30-year rate, that causes the 15-year rate to rise as well. Interest rates are determined by economic conditions. When economic conditions cause 30-year rates to increase, these same conditions cause 15-year rates to increase as well. . When a bank increaes the 15-year rate, that causes the 30-year rate to rise as well. 7. As of July, 2013, 28 states in the U.S. had one or more tribal gambling casinos. The following data presents the number of tribal casinos in each of those states [4 pts] 32 26 70 2 2 8 7 3 4 3 22 39 3 14 7 3 21 8 2 11 114 8 14 1 34 31 4 (a) Find the first and third quartiles of these data. (b) Find the Median of these data. (c) Find the upper and lower outlier boundaries. (d) Which values, if any, are outliers? (e) Construct a boxplot for these data. (f) Describe the shape of this distribution. (g) What is the 40th percentile? (h) What is the 83rd percentile? (i) North Dakota has 11 tribal casinos. What percentile is this? (j) What is the mode?