If the estimated slope coefficient is = - 5.45 and the standard error for the slope coefficient is 1.75, which of the following is true using a 95 percent confidence level?
A)The null hypothesis is rejected and you can be 95 percent confidence that the true slope coefficient is not equal to zero.
B)The null hypothesis is not rejected and you can be 95 percent confidence that the true slope coefficient is equal to zero.
C)The null hypothesis is not rejected and you can be 95 percent confidence that the true slope coefficient is not equal to zero.
D)The null hypothesis is rejected and you can be 95 percent confidence that the true slope coefficient is equal to zero.

Question

If the estimated slope coefficient is  = - 5.45 and the standard error for the slope coefficient is 1.75, which of the following is true using a 95 percent confidence level?
A)The null hypothesis is rejected and you can be 95 percent confidence that the true slope coefficient is not equal to zero. 
B)The null hypothesis is not rejected and you can be 95 percent confidence that the true slope coefficient is equal to zero. 
C)The null hypothesis is not rejected and you can be 95 percent confidence that the true slope coefficient is not equal to zero. 
D)The null hypothesis is rejected and you can be 95 percent confidence that the true slope coefficient is equal to zero.

Quizplus · Accepted Answer

With a 95 percent confidence level, the critical value for a two-tailed test is 1.96. The estimated slope coefficient (-5.45) divided by the standard error of the slope coefficient (1.75) gives a t-statistic of -3.11. Since the absolute value of the t-statistic is greater than 1.96, we reject the null hypothesis that the true slope coefficient is equal to zero. Therefore, we can be 95 percent confident that the true slope coefficient is not equal to zero.

If the Estimated Slope Coefficient Is = - 5