Astatistics 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 excel’s data analysis, he obtained the following result.

r2=0.23

coefficient standard error
intercept 25675.5 11393
x 5321 2119

what is the p-value?

select one:

a. 0.02
b. 0.01
c. 0.17
d. 0.34

Step-by-step explanation:

Hello!

Given the linear regression of Y: "Annual salary" as a function of X: "Mean score on teaching evaluation" of a population of university professors. It is desired to study whether student evaluations are related to salaries.

The population equation line is

E(Y)= β₀ + β₁X

Using the information of a n= 100 sample, the following data was calculated:

R²= 0.23

                Coefficient    Standard Error  

Intercept    25675.5           11393

x                  5321                  2119

The estimated equation is

^Y= 25675.5 + 5321X

Now if the interest is to test if the teaching evaluation affects the proffesor's annual salary, the hypotheses are:

H₀: β = 0

H₁: β ≠ 0

There are two statistic you can use to make this test, a Student's t or an ANOVA F.

Since you have information about the estimation of  β you can calculate the two tailed t test using the formula:

~

= 25.1109

The p-value is two-tailed, and is the probability of getting a value as extreme as the calculated under the distribution

p-value < 0.00001

I hope it helps!