Consider the following to answer the question(s) below:
National birth rates (births per 1,000) may be influenced by the average national life expectancy in years and the national literacy rate (% of population that can read and write). Data for 49 countries were obtained and the regression results follow.
-Suppose that Life Expectancy is the first variable and Literacy Rate is the second variable. The correct alternative hypothesis for the overall significance for this model is
A) HA: at least one β ≠ 0.
B) HA: β1 = β2 = 0.
C) HA: β1 = 0.
D) HA: β2 = 0.
E) HA: all β ≠ 0.

Question

Consider the following to answer the question(s) below:
National birth rates (births per 1,000) may be influenced by the average national life expectancy in years and the national literacy rate (% of population that can read and write). Data for 49 countries were obtained and the regression results follow. 
-Suppose that Life Expectancy is the first variable and Literacy Rate is the second variable. The correct alternative hypothesis for the overall significance for this model is
A) HA: at least one β ≠ 0. 
B) HA: β1 = β2 = 0. 
C) HA: β1 = 0. 
D) HA: β2 = 0. 
E) HA: all β ≠ 0.

Quizplus · Accepted Answer

The correct alternative hypothesis for the overall significance of the model is that at least one of the regression coefficients (β1 and β2) is not equal to 0. This is represented by choice A, which states HA: at least one β ≠ 0. The other choices are incorrect because they either suggest that both regression coefficients are equal to 0 (B), that only one of the coefficients is equal to 0 (C and D), or that all coefficients are not equal to 0 (E).

Consider the Following to Answer the Question(s) Below