Question

Suppose you would like to test the hypothesis that one year of attending a university is worth three years of attending a two-year school (junior college), in terms of effect on wages, using the following econometric model:log(wage)=β0+β1jc+β2univ+β3exper + uwhats the Null?

Answer 1

`H_(0) : \beta_(2) = 3 \beta_(1)`

Step-by-step explanation:

A null hypothesis (
`H_(0))` is a hypothesis that says there is no statistical significance between the two variables. It is usually the hypothesis a researcher or experimenter will try to disprove or discredit.

An alternative hypothesis
`(H_(a) )` is a hypothesis that states there is a statistically significant relationship between two variables.

In this example, the hypothesis to test is that one year of attending a university is worth 3 years of attending a two-year junior college

If
`\beta_(2) =` the number of years of attending a university, and

`\beta_(1) =` the number of years of attending a junior college

Since 3 years of attending the junior college is equivalent to 1 year of attending the university, the null hypothesis is given by:

`H_(0) : \beta_(2) = 3 \beta_(1)`

Answer 2

`H_0: \beta_2 = 3\beta_1`

Step-by-step explanation:

The null hypothesis is the hypothesis that there is no significant difference between specified populations and that any observed difference is due to sampling/experimental error.

We would like to test that one year of attending a university with regression parameter
`\beta_2` is worth 3 years of attending a junior college with regression parameter
`\beta_1` in terms of the wages earned.

In the model:
`log(wage)=\beta_0+\beta_1jc+\beta_2univ+\beta_3exper + u`

The null hypothesis will therefore be:

`H_0: \beta_2 = 3\beta_1`