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 50 randomly selected cadavers from Gladstone's study, where X is the predictor variable head size and Yˆ is the predicted response variable brain weight. The standard error of the slope coefficient for this model, SEb, is 0.0233. Yˆ=342.0134+0.2585X

Using this regression line, suppose Gladstone wishes to conduct a two‑tailed t ‑test to test the hypothesis that subjects with larger head sizes will have either smaller or larger brain weights. Let =0.05 and assume that all of the necessary conditions are met for this linear regression model. Let β represent the slope of the population regression line.

Required:
Compute the t-statistic and its corresponding.