An Academic Advisor Wants to Predict the Typical Starting Salary $$\hat { \beta } _ { 0 } = - 92040 \hat { \beta } 1 = 228 \mathrm {~s} = 3213 \mathrm { df } = 23 \quad t = 6.67$$

An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT using 25 data points is shown below.
$$\hat { \beta } _ { 0 } = - 92040 \hat { \beta } 1 = 228 \mathrm {~s} = 3213 \mathrm { df } = 23 \quad t = 6.67$$
Set up the null and alternative hypotheses for testing whether a linear relationship exists between SALARY and GMAT.

A) $H _ { 0 } : \beta _ { 1 } = 0$ vs. $H _ { \mathrm { a } } : \beta _ { 1 } > 0$
B) $H _ { 0 } : \beta 1 = 0$ vs. $H _ { \mathrm { a } } : \beta 1 \neq 0$
C) $H _ { 0 } : \hat { \beta } 1 = 228$ vs. $H _ { \mathrm { a } } : \hat { \beta } _ { 1 } > 228$
D) $H _ { 0 } : \beta _ { 1 } > 0$ vs. $\mathrm { H } _ { \mathrm { a } } : \beta _ { 1 } < 0$