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 = -2.56
B) z = 2.639
C) t = 2.56
D) t = 2.639

Question

Quizplus · Accepted Answer

Since the sample size is small (n < 30) and the population standard deviation is unknown, we need to use a t-test to test the significance of the slope. The test statistic is calculated as: t = (b - β) / SE(b), where b is the estimated slope (2.56), β is the null hypothesis slope (usually 0), and SE(b) is the standard error of the slope (0.97). Substituting the values, we get t = (2.56 - 0) / 0.97 = 2.639. Therefore, the correct answer is D.

The Regression Equation Is Ŷ = 30 + 2