A statistics practitioner in a large university is investigating the factors that affect salary of professors. He wondered if ev

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2 months ago

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A statistics practitioner in a large university is investigating the factors that affect salary of professors. He wondered if ev

aluations 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

Mathematics

1 answer:

tester [12.3K] · Answer 1 · 2026-03-17T21:20:18+03:00

In this context, we analyze a linear regression where Y is the variable "Annual salary" predicted by X, which denotes "Mean score on teaching evaluation" for university professors. The goal is to ascertain whether there is a correlation between student evaluations and professor salaries. The population regression equation can be stated as E(Y)= β₀ + β₁X. Given an n = 100 sample, data shows an R² of 0.23. Further statistical calculations yield the estimated equation as ^Y= 25675.5 + 5321X. To verify if teaching evaluations impact salaries, the null and alternative hypotheses are H₀: β = 0 and H₁: β ≠ 0. A two-tailed t-test can be performed, with the calculated t-value being approximately 25.1109. The resulting two-tailed p-value is found to be significantly less than 0.00001.