Question

# You are testing the null hypothesis that there is no linear relationship between two variables, X...

You are testing the null hypothesis that there is no linear relationship between two variables, X and Y. From your sample of n=11, you determine that r =0.55.

a. What is the value of tSTAT?

b. At the α =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?

a. What are the hypotheses to test?

a. H0: ρ ≥0 H1: ρ <0    b. H0: ρ =0 H1: ρ ≠0

c. H0:ρ ≠0 H1: ρ =0 d. H0:ρ ≤0 H1: ρ >0

tStat= ____

(Round to four decimal places as needed.)

b. The lower critical value is_______ .

(Round to four decimal places as needed.)

The upper critical value is ________.

Round to four decimal places as needed.)

c. What statistical decision should you make?

A. Since tSTAT is greater than upper critical value, reject H0.

B. Since tSTAT is greater than upper critical value, do not reject H0.

C. Since tSTAT is between the critical values, reject H0.

D. Since tSTAT is between the critical values, do not reject H0.

To Test :-

H0: ρ =0

H1: ρ ≠0

Test   Statistic :-

t = 1.9757

Test   Criteria :-
Reject   null hypothesis if       OR

-2.685 < 1.9757 < 2.685
Result :- We fail to Reject null hypothesis

Decision based on P value
P - value = 0.0796
Reject null hypothesis if P value <    level of significance
P - value = 0.0796 > 0.05 ,hence we fail to reject null hypothesis

Lower Critical value = - 2.685

Upper critical value = 2.685

D. Since tSTAT is between the critical values, do not reject H0.