Question

Listed below are the overhead widths​ (in cm) of seals measured from photographs and the weights​ (in kg) of the seals. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the critical values of r using

α=0.05. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the​ seals?

Overhead Width	7.1	7.6	9.9	9.3	8.7	8.2
Weight	113	177	250	199	199	187

Construct a scatterplot. Choose the correct graph below.

The critical values are

Because the absolute value of the linear correlation coefficient is?

Answer 1

Part a)

r = 0.9161

To Test :-

H0 :- ρ = 0
H1 :- ρ ≠ 0

Test Statistic :-
t = (r * √(n - 2) / (√(1 - r2))
t = ( 0.9369 * √(10 - 2) ) / (√(1 - 0.8777) )
t = 7.5775

Critical value  t(α/2,n-2) = t(0.05/2 , 10 - 2 ) = 2.306

t < -2.306 OR t > 2.306

Test Criteria :-
Reject null hypothesis if t > t(α/2,n-2)
t(α/2,n-2) = t(0.05/2 , 10 - 2 ) = 2.306
t > t (α/2, n-2) = 7.5775 > 2.306
Result :- Reject null hypothesis

Decision based on P value
P - value = P ( t > 7.5775 ) = 0.0001
Reject null hypothesis if P value < α = 0.05 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.