Question

The following data represent the weight of a child riding a bike and the rolling distance achieved after going down a hill without pedaling.

Weight (lbs.)	Rolling Distance (m.)
59	26
83	43
97	49
56	20
103	65
87	44
88	48
91	42
52	39
63	33
71	39
100	49
89	55
103	53
99	42
74	33
75	30
89	30
102	40
103	33
99	33
102	35
86	37
85	37

Can it be concluded at a 0.01 level of significance that there is a linear correlation between the two variables?

• A.

  yes, the p-value = .00001

• B.

  no, the p-value = .00001

• C. Cannot be determined

• D. yes, the p-value = .0055

• E. no, the p-value = .0055

Answer 1

r = .5487

To Test :-

H0 :- ρ = 0
H1 :- ρ ≠ 0

Test Statistic :-
t = (r * √(n - 2) / (√(1 - r2))
t = ( 0.5487 * √(24 - 2) ) / (√(1 - 0.3011) )
t = 3.0785
Test Criteria :-
Reject null hypothesis if t > t(α/2,n-2)
t(α/2,n-2) = t(0.01/2 , 24 - 2 ) = 2.8188
t > t (α/2, n-2) = 3.0785 > 2.8188
Result :- Reject null hypothesis

Decision based on P value
P - value = P ( t > 3.0785 ) = 0.0055
Reject null hypothesis if P value < α = 0.01 level of significance
P - value = 0.0055 < 0.01 ,hence we reject null hypothesis
Conclusion :- We reject H0

D. yes, the p-value = 0.0055