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 56 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, SEb, is 0.0228.
y = 262.4646 + 0.2804x
Using this regression line, suppose Gladstone wishes to conduct a one-tailed test for no linear relationship to test the hypothesis that subjects with larger head sizes will also have larger brain weights. Let α = 0.05 and assume that all of the necessary conditions are met for this linear regression model. Let B represent the slope of the population regression line.
Select the correct null hypothesis, Ho, and alternative hypothesis, Ha, for Gladstone's one-tailed t-test:
Ho: B = 0 and Ha: B > 0
Compute the t-statistic and its corresponding degrees of freedom, df, for this one-tailed t-test. Please round your t-statistic to three decimal places.
df