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Since obtaining measurements of the human brain is difficult with living subjects, Gladstone (1905) used cadavers to investigate if there was a relationship between a subject's head size (in cubic centimeters) and his or her brain weight (in grams). This linear regression model was fit using 52 randomly selected cadavers from Gladstone's study, where x is the predictor variable head size and y is the predicted response variable brain weight. The standard error of the slope coefficient for this model, SE, is 0.0261. y = 407.3294 + 0.2374x Using this regression line, suppose Gladstone wishes to conduct a one-tailed f-test for no linear relationship to test the hypothesis that subjects with larger head sizes will also have larger brain weights. Let a = 0.05 and assume that all of the necessary conditions are met for this linear regression model. Let / represent the slope of the population regression line. Select the correct null hypothesis, Ho, and alternative hypothesis, Ha, for a one-tailed f-test. O Ho : f = 0 and H. : 8>0 O Ho : p = 0.2374 and Ha : p > 0.2374 O Ho : / = 0 and Ha : 8 0 O Ho : p = 407.3294 and Ha : ( > 407.3294 O Ho : r = 0 and Ha :r> 0 Compute the f-statistic and its corresponding degrees of freedom, df, for this one-tailed f-test. Please round your f-statistic to three decimal places. 1 =df = Assuming a = 0.05, use software or a f-table to determine if Gladstone should reject or fail to reject the null hypothesis from his one-tailed f test. Select the correct statement. Gladstone should fail to reject Ho because the P-value > a. Gladstone should reject Ho because the P-value > a. Gladstone should reject Ho because the P-value