1. cont... e. f. g.1. cont... h. 40 42 44 46 48 8 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 AGEl. A doctor knows that muscle mass decreases with age. To help him understand this relationship in women, the doctor selected women beginning with age 40 and ending with age 80. The data is given in the table below. x is age, y is a measure of muscle mass {the higher the measure, the more muscle mass). a. Use your calculator to make a scatter plot that shows how age helps explain muscle mass. Does there appear to be a linear relationship? Find the Pearson sample correlation coefcient, r. What does 1" tell you about the strength of the relationship? At the 1% level of signicance, perform a hypothesis test to test the signicance of the correlation coefcient. Use your scatter plot's shape to determine the form of the alternative hypothesis. Find the least squares regression equations Interpret slope and y-intercept in context of the problem. Be sure to graph this regression equation within your scatter plot to make sure your equations appears to \"best t\" the data. Predict the muscle mass for women aged 60 years. Is the predicted value in part d. an interpolated or extrapolated value? Explain. If the muscle mass of a woman was determined to be 58, what age does the model predict she would be? Would you trust the model's prediction for the value you calculated in part i? Why or why not? In order to help you have more \"good faith\" in your model, create a residual plot. You must plot the original x-values(AGE} along with the residuals as Y-values(Residual = y y'). Are there any patterns in the residual plot that would make you \"second guess\" your original assumption of linearity? x 3' (Age) (Muscle Mass} 1"? I53 63 86 46 105 5? T3 44 95 51 190 40 l 12 80 T5 Answer Pages 1. a. 120 115 110 105 M 100 95 90 M 85 80 75 70 65 60 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 2 74 76 78 80 AGE1. cont... b. Hypothesis Test: Ho: p = 0 Ha: P 0 0 = Testing Statistic: 1 = - run-2 df = n - 2 = Critical Value: to = ( from Table III) r = p-value: Result of Test: Conclusion: Based on the given information... C. D