Set up the null and alternative hypotheses for testing whether a positive linear relationship exists between SALARY and GMAT in the situation above. A) $H _ { 0 } : \beta _ { 1 } = 228$ vs. $H _ { \mathrm { a } } : \beta _ { 1 } 228$ B) $H _ { 0 } : \beta _ { 1 } 0$ vs. $H _ { \mathrm { a } } : \beta _ { 1 } 0$ D) $H _ { 0 } : \beta 1 = 0$ vs. $H _ { \mathrm { a } } : \beta _ { 1 } \neq 0$

Question

Set up the null and alternative hypotheses for testing whether a positive linear relationship exists between SALARY and GMAT in the situation above.
A) $H _ { 0 } : \beta _ { 1 } = 228$ vs. $H _ { \mathrm { a } } : \beta _ { 1 } > 228$
B) $H _ { 0 } : \beta _ { 1 } > 0$ vs. $H _ { \mathrm { a } } : \beta _ { 1 } < 0$
C) $H _ { 0 } : \beta _ { 1 } = 0$ vs. $H _ { \mathrm { a } } : \beta _ { 1 } > 0$
D) $H _ { 0 } : \beta 1 = 0$ vs. $H _ { \mathrm { a } } : \beta _ { 1 } \neq 0$

Quizplus · Accepted Answer

To test for a positive linear relationship, the null hypothesis should state there is no relationship ($\beta_1 = 0$), and the alternative should suggest a positive relationship ($\beta_1 > 0$).

Set Up the Null and Alternative Hypotheses for Testing Whether H0:β1=228H _ { 0 } : \beta _ { 1 } = 228H0​:β1​=228

Set Up the Null and Alternative Hypotheses for Testing Whether $H _ { 0 } : \beta _ { 1 } = 228$