Question

Please show all work and explain.

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 = +4.5 and S_b1= 1.5. The value of t stat = coefficient/std error = 3.

a) At the α = 0.05 level of significance, what are the critical values?

b) Based on the information and your answer, what statistical decision should you make?

Answer 1

Solution:

Given:

Sample size = n = 18

b₁ = +4.5 and S_b1= 1.5.

The value of t stat = coefficient/std error = 3.

We have to test  the null hypothesis that there is no linear relationship between two variables X and Y.

Thus hypothesis of the study are:

( there is no linear relationship between two variables X and Y)

Vs

( there is significant linear relationship between two variables X and Y)

Part a) At the α = 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 b) Based on the information and your answer, what statistical decision should you make?

Since t test statistic value = 3 > t critical value = 2.120, we reject null hypothesis H0.

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