Question

You are testing the null hypothesis that there is no linear relationship between two variables, X and Y. You are given the following regression results, where the sample size is 10.,

	Coefficient	Standart error
Intercept	-1.2	1
X	2	2

a) What is the value of the t test statistic?

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

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

Answer 1

We know that:

Null hypothesis: H0: Beta = 0

Alternate hypothesis: Ha: Beta not= 0

a.

We also know that b=2

Standard error= 2

Thus, test statistic, t= (2-0)/2= 2/2= 1

b.

We know that the degrees of freedom= n-1= 9

Also, the level of significance= 0.05/2= 0.025

Thus, t_{0.025, 9}= 2.26

c.

Since the test statistic is within the acceptance region (-2.26 to 2.26), we fail to reject the null hypothesis and conclude that there is no linear relationship between the variables.