Consider the regression results from the regression of Y against X for 50 observations: Y = 0.78 + 1.2 X The standard error of the estimate is 0.40 and the standard error of the coefficient is 0.45. Which of the following reports the correct value of the t-statistic for the slope and correctly evaluates its statistical significance with 95% confidence? A) t = 2.667; slope is significantly different from zero. B) t = 3.000; slope is significantly different from zero. C) t = 1.789; slope is not significantly different from zero. The test statistic is t = (1.2 – 0) / 0.45 = 2.667. The critical t-values for 48 degrees of freedom are ± 2.011. Therefore, the slope is different from zero. I’m wondering, how did they get the critical t-values for 48 degrees of freedom ± 2.011? The t table only gives you the df of 40, 60 and 120.
Approximation To be even more precise: t(critical[48,0.05]) = 2.0106 as per http://davidmlane.com/hyperstat/t_table.html