Question

A statistics practitioner in a large university is investigating the factors that affect salary of professors. He wondered if evaluations by students are related to salaries. To this end, he collected 100 observations on:

y = Annual salary (in dollars)
x = Mean score on teaching evaluation

To accomplish his goal, he assumes the following relationship:

y = β(0) + β(1)x + ε

Then, using Data Analysis, he obtained the following result.
R2=0.23

Coefficient Standard Error
Intercept 25675.5 11393
x 5321 2119

Required:
What are the null and alternative hypotheses, respectively?

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

The null hypothesis is
`H_0 : \beta_1 = 0`

The alternative hypothesis is
`H_1 : \beta_1 \\e 0`

Explanation:

From the question we are told that

The number observations is
`n = 100`

The annual salary (in dollars) is y

The mean score on teaching evaluation is x

The the relationship between the y and x is

`y = \beta_0 + \beta_1 x + \epsilon`

From this mathematical relationship we see that
`\beta_1` is the mean

So

The null hypothesis is
`H_0 : \beta_1 = 0` [i.e evaluations does not affect salary]

The alternative hypothesis is
`H_1 : \beta_1 \\e 0` [ i.e evaluations affect salary ]