In a study of reaction times,) $\begin{array}{cc}
\hline \text { Visual } & \text { Auditory } \
\hline 208 & 249 \
200 & 244 \
245 & 254 \
234 & 249 \
155 & 243 \
211 & 248 \
189 & 244 \
206 & 247 \
\hline
\end{array}$
Test $H _ { 0 } : \beta _ { 1 } = 0$ versus $H _ { 1 } : \beta _ { 1 } \neq 0$. Use the $\alpha = 0.05$ level of significance.
A) Do not reject $H _ { 0 }$.
B) Reject $H _ { 0 }$.

Question

Quizplus · Accepted Answer

The hypothesis $H_0: \beta_1 = 0$ versus $H_1: \beta_1 \neq 0$ concerns the slope of the regression line in a linear regression model, where $\beta_1$ represents the effect of the independent variable (Visual) on the dependent variable (Auditory). Without performing the specific calculations (which would involve calculating the regression line, the standard error, the t-statistic, and comparing it to a critical value from the t-distribution at $\alpha = 0.05$), the decision to reject $H_0$ suggests that there is statistically significant evidence at the 0.05 level to conclude that there is a non-zero relationship between the visual and auditory reaction times. This conclusion is based on the principles of hypothesis testing in the context of linear regression analysis.

In a Study of Reaction Times,) Test H0:β1=0H _ { 0 } : \beta _ { 1 } = 0H0​:β1​=0

In a Study of Reaction Times,) Test $H _ { 0 } : \beta _ { 1 } = 0$