If the t-stat for the sample estimate of a coefficient, M₁ calculated as the following, t = $\frac { m _ { 1 } } { S _ { m _ { 1 } } }$ , where m₁ is the estimated coefficient and S $m _ { 1 }$ is the properly estimated standard error for the coefficient, comes out to be 2.7, what is the appropriate conclusion? A) Reject the null hypothesis that the population coefficient M₁ = 0 at a 99% confidence level. B) Fail to reject the null hypothesis that the population coefficient M₁ = 1 at a 95% confidence level. C) Reject the null hypothesis that the population coefficient M₁ = 2 at a 99% confidence level. D) None of these choices are correct.

Question

Quizplus · Accepted Answer

The t-statistic of 2.7 indicates that the estimated coefficient is 2.7 standard errors away from the null hypothesis value of 0. At a 99% confidence level, the critical t-value is 2.58 for a two-tailed test. Since the calculated t-statistic of 2.7 is higher than the critical t-value of 2.58, we reject the null hypothesis that the population coefficient M₁ = 0.

If the T-Stat for the Sample Estimate of a Coefficient m1Sm1\frac { m _ { 1 } } { S _ { m _ { 1 } } }Sm1​​m1​​

If the T-Stat for the Sample Estimate of a Coefficient $\frac { m _ { 1 } } { S _ { m _ { 1 } } }$