Question

For a sample of eight​ bears, researchers measured the distances around the​ bears' chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is r=0.963. Using α=​0.05, determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest​ size? What is the test statistic? (round to three decimals)

Answer 1

n = 8

r = 0.963

Coefficient of Determination

Explained variation = 0.927* 100 = 92.7%
Unexplained variation = 1 - 0.927* 100 = 7.3%

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


t = 8.755

Test Criteria :-
Reject null hypothesis if


Result :- Reject null hypothesis

Decision based on P value
P - value = P ( t > 8.7545 ) = 0.0001
Reject null hypothesis if P value < level of significance
P - value = 0.0001 < 0.05 ,hence we reject null hypothesis
Conclusion :- We reject H0

There is statistically linear correlation between variables chest size and weight.