Question

Suppose you find that: y=β0​+β1​x1​+β2​x2​+β3​x3​ HRSWORK =33.026−0.03572 WAGE+ 0.615EDUC−0.45012 NCHILD (1.216)(0.0176)(0.0894)(0.1951)​ HRSWORK hours worked by an average woman WAGE: woman's wage EDUC: years of education NCHILD: number of children the woman has a) Specify the null and alternate hypothesis to test if wage has an effect on hours worked. Is this a one-tailed or two-tailed test?

Answer 1

• The null and alternative hypotheses are specified for testing the effect of wage on hours worked.
• This is a two-tailed test.

Step-by-step explanation:

The null hypothesis (H₀) for testing if wage has an effect on hours worked is that wage does not affect hours worked. This is represented as H₀: β1 = 0, where β1 is the coefficient for the variable WAGE in the regression equation.

The alternative hypothesis (Ha) is that wage does have an effect on hours worked. This is represented as Ha: β1 ≠ 0, indicating that the coefficient for WAGE is not equal to zero.

In this case, the alternative hypothesis is testing for a two-sided effect. This means that we are interested in determining if there is a significant difference in either direction (positive or negative) between wage and hours worked. The alternative hypothesis does not specify a particular direction of the effect.

Therefore, this is a two-tailed test.

The random variable of interest for this test is hours worked (HRSWORK). We want to investigate if there is a significant relationship between wage and the number of hours worked by an average woman.