A manager at a local bank analyzed the relationship between monthly salary (y,in $)and length of service (x,measured in months)for 30 employees.She estimates the following model: Salary = β₀ + β₁ Service + ε.The following table summarizes a portion of the regression results. Which of the hypotheses will determine whether the slope differs from zero? A) H₀:β₀ = 0;H_A: β₀ ≠ 0 B) H₀:β₁ = 0;H_A: β₁ ≠ 0 C) H₀:b₀ = 0;H_A: b₀ ≠ 0 D) H₀:b₁ = 0;H_A: b₁ ≠ 0

Question

Quizplus · Accepted Answer

The hypothesis H₀: β₁ = 0; H_A: β₁ ≠ 0 will determine whether the slope differs from zero. This is because the coefficient β₁ represents the change in salary for a one-unit increase in service, which is the slope of the regression line. The null hypothesis H₀: β₁ = 0 states that there is no linear relationship between salary and service, meaning that the slope is zero. The alternative hypothesis H_A: β₁ ≠ 0 states that there is a linear relationship between salary and service, meaning that the slope is not zero. Therefore, hypothesis testing for β₁ will determine whether the slope differs from zero.

A Manager at a Local Bank Analyzed the Relationship Between