Question

A study of bone density on 5 random women at a hospital produced the following results.

Age	53	57	61	69	73
Bone Density	355	350	345	325	315

Step 1 of 3 :  Calculate the correlation coefficient, r. Round your answer to six decimal places.

Step 2 of 3: Determine if r is statistically significant at the 0.01 level.

Step 3 of 3: Calculate the coefficient of determination, r^2. Round your answer to three decimal places.

Answer 1

X :- Age

Y :- Bone density

ΣX = 313
ΣY = 1690
ΣX * Y = 105230
ΣX2 = 19869
ΣY2 = 572400

Step 1

r = -0.98972

Step 2

To Test :-
H0 :- ρ = 0
H1 :- ρ ≠ 0

Test Statistic :-
t = (r * √(n - 2) / (√(1 - r2))
t = ( -0.9897 * √(5 - 2) ) / (√(1 - 0.9795) )
t = -11.9726

Test Criteria :-
Reject null hypothesis if t < -t(α,n-2)
t(α/2,n-2) = t(0.01/2 , 5 - 2 ) = 5.841
t < -t(α/2, n-2) = -11.9726 < -5.841
Result :- Reject null hypothesis
Conclusion :- There is statistical correlation between variables.

Step 3

Coefficient of Determination