A County Real Estate Appraiser Wants to Develop a Statistical $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x ,$$

Short Answer

A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model: $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x ,$$
where $y =$ appraised value of the house (in thousands of dollars) and $x =$ number of rooms.

What set of hypotheses would you test to determine whether appraised value is positively linearly related to number of rooms?
A) $H _ { 0 } : \beta _ { 1 } = 0$ vs. $H _ { \mathrm { a } } : \beta _ { 1 } > 0$
B) $H _ { 0 } : \beta _ { 1 } < 0$ vs. $H _ { a } : \beta _ { 1 } > 0$
c) $H _ { 0 } : \beta _ { 1 } = 0$ vs. $H _ { a } : \beta _ { 1 } < 0$
D) $H _ { 0 } : \beta _ { 1 } = 0$ vs. $H _ { \mathrm { a } } : \beta _ { 1 } \neq 0$