Question

Listed below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of a = 0.05. 79.7 57.3 Internet Users Award Winners 80.1 5.6 68.2 1.8 76.6 11.1 39.1 0.1 9.3 3.3

Answer 1

X - Internet users

Y :- Award winners

ΣX = 401
ΣY = 31.2
ΣX * Y = 2355.79
ΣX2 = 28099
ΣY2 = 255.2

Scatter Plot 12 10 8 6 4 2 . 0 0 10 20 30 40 50 60 70 80 90

((N + ΣΧΥ) - ΣΧΣΥ)/((ΝΣ(Χ2) - (ΣΧ)2] (ΝΣ(Y2) – (ΣΥ)2)


7 ((6*2355.79)-401*31.2)/(16* 28099) – (401)2)(6 * 255.2) – (31.2)2)

r = 0.779

To Test :-
H0 :- ρ = 0
H1 :- ρ ≠ 0

Test Statistic :-
t = (r * √(n - 2) / (√(1 - r2))
t = ( 0.7787 * √(6 - 2) ) / (√(1 - 0.6064) )
t = 2.48

P - value = P ( t > 2.482 ) = 0.068

Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.068 > 0.05, hence we fail to reject null hypothesis
Conclusion :- There is no statistical correlation between variables

P value is greater than α, there is not sufficient evidence to support the claim.