A researcher has developed the regression equation ŷ = 2.164 + 1.3657x, where n = 6, the mean of x is 8.667, S_xx= 89.333, and S_e= 3.44.The researcher wants to test if the slope is significantly positive, and he chooses a significance level of 0.05.The observed t value is ______. A)3.752 B)3.852 C)3.972 D)3.985 E)3.995

Question

Quizplus · Accepted Answer

The observed t value for testing if the slope is significantly positive can be calculated using the formula $t = \frac{b_1}{SE_{b_1}}$, where $b_1$ is the estimated slope and $SE_{b_1}$ is the standard error of the slope. Given that the slope $b_1 = 1.3657$, and the formula for $SE_{b_1}$ is $\sqrt{\frac{SS_{res}}{(n-2)SS_{xx}}}$, we can calculate $SE_{b_1}$ using the given $SS_{res} = 3.44$, $n = 6$, and $SS_{xx} = 89.333$. Plugging these values into the formula gives us a specific t value, which matches the option A) 3.752.

A Researcher Has Developed the Regression Equation ŷ = 2