Question

A data set includes weights of garbage discarded in one week from 62 different households. The paired weights of paper and glass were used to obtain the results shown to the right. Is there sufficient evidence to support the claim that there is a linear correlation between weights of discarded paper and​ glass? Use a significance level of α=0.05.

1	0.3731
0.3731	1

Identify critical values and test statistic

Answer 1

null hypothesis: Ho:               ρ		=	0
Alternate Hypothesis: Ha: ρ		≠	0
0.05 level,two tail test and n-2= 60 df, critical t=			2.000
Decision rule: reject Ho if absolute value of test statistic |t|>2.000

correlation coefficient r=		Sxy/(√Sxx*Syy) =	0.3731
test stat t=	r*(√(n-2)/(1-r2))=	3.1149

since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to conclude that there is a linear correlation between weights of discarded paper and​ glass