Question

You are testing the null hypothesis that there is no linear relationship between two​ variables, X and Y. From your sample of n=18, you determine that b1=4.4 and Sb1=1.3

a. What is the value of t stat?

b. At the a=0.05 level of​ significance, what are the critical​ values?

c. Based on your answers to​ (a) and​ (b), what statistical decision should you​ make?

d. Construct a​ 95% confidence interval estimate of the population​ slope,β1.

Answer 1

Solution:

Given:

Sample size = n = 18

b₁=4.4 and S_b1=1.3

Part a. What is the value of t stat?

Part b. At the a=0.05 level of​ significance, what are the critical​values?

df = n - 2 = 18 - 2 = 16

Look in t table for df = 16 and two tail area = 0.05 and find t critical values.

t critical values = ( -2.120 , 2.120 )

Part c. Based on your answers to​ (a) and​ (b), what statistical decision should you​ make?

Since t test statistic value = 3.385 > t critical value = 2.120, we reject null hypothesis H0.

Thus there is significant  linear relationship between two variables X and Y.

Part d. Construct a​ 95% confidence interval estimate of the population​ slope,β1.

Formula:

where

Thus

Thus a​ 95% confidence interval estimate of the population​ slope,β1 is between: