Question

There seemed to be a negative linear correlation between air pressure (in kiloPascals) and McNabb’s throwing distance (in yards). Data follows:

Air Pressure in Stadium (kPa), x 101.2 101.6 102 102.4 103 103 103.5 104 104.2 104.3 Distance Football Thrown (yards), y 56 58 58 57 56 55 54.5 55.5 56 55 Also, the data has partially been processed to provide: X = 102.92 y = 56.1 (x; -7)(y;-5)=-7.870 {(x; - x)² = 10.876 (y; -y)} = 13.400 Perform a hypothesis test on the hypotheses: H, :p = 0 HA:P < 0 Please compute the value of the test statistic. Should the null hypothesis be rejected at a = 0.05?

Answer 1

null hypothesis: Ho:           ρ'=		0
Alternate Hypothesis: Ha: ρ<		0
0.05 level,left tail test and n-2= 8 df, critical t=-1.860			(from excel:tinv(0.1,8)
Decision rule: reject Ho if test statistic t<-1.860

correlation r='Sxy/(√Sxx*Syy) =-7.87/sqrt(10.876*13.400)=		-0.652
test stat t=	r*(√(n-2)/(1-r2))=-2.4316

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that there is a negative correlation between two variables.