The regression equation is Ŷ = 30 + 2.56X,the sample size is 14,and the standard error of the slope is 0.97. What is the test statistic to test the significance of the slope?
A)z = −2.560
B)z = +2.639
C)t = +2.560
D)t = +2.639

Question

Quizplus · Accepted Answer

To test the significance of the slope, we need to calculate the t-statistic using the formula: 
t = (b - 0) / SEb 
where b is the regression coefficient (slope), SEb is the standard error of the slope, and 0 is the hypothesized value of the slope (in this case, it is 0 because we want to test if the slope is significantly different from 0). 
Substituting the given values: 
t = (2.56 - 0) / 0.97 = 2.639 
Since the sample size is 14, the degrees of freedom are n-2 = 12. Using a t-distribution table with 12 degrees of freedom, the critical value for a two-tailed test at 5% level of significance is ±2.179. Since our calculated t-statistic (2.639) is greater than the critical value (2.179), we can reject the null hypothesis and conclude that the slope is significantly different from 0. Hence, the answer is D.

The Regression Equation Is Ŷ = 30 + 2