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  $H_1 : \beta_1 \ne 0$

Step-by-step 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  $H_1 : \beta_1 \ne 0$ [ i.e evaluations  affect salary ]