Question

PROBLEM #1: (Multiple Choice) Choose the correct answer. We conduct a regression analysis to test the hypotheses β = 1 vs H_a: β = 1. The value of the test statistic is found to be 2.24 for sample sizes n=22. The p-value for this test is:

⑴ 0.01 < p-value < 0.025

⑵ 0.02 < p-value < 0.05

⑶ 0.0005 < p-value < 0.001

⑷ 0.001 < p-value < 0.005

⑸ None of the above

Answer 1

Solution:
Given:

A regression analysis is conducted to test the hypotheses β = 1 vs H_a: β   1.

The value of the test statistic is found to be 2.24 for sample sizes n=22.

thus t test statistic = 2.24

and df = n - 2

df = 22- 2

df = 20

Look in t table for df = 20 row and find an interval in which t = 2.24 fall.

Then find corresponding two tail area interval ( two tail , since this is two tailed test), which is p-value interval.

t = 2.24 fall between 2.086 and 2.528.

Corresponding two tail area is between 0.02 and 0.05

Thus we get:

0.02 < p-value < 0.05

Thus correct answer is:

(2) 0.02 < p-value < 0.05