For a sample of eight bears, researchers measured the distances around the bears' chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is requals0.952. Using alphaequals0.05, determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?
Accepted Solution
A:
Answer:Step-by-step explanation:Given that for a sample of eight bears, researchers measured the distances around the bears' chests and weighed the bears. r = linear correlation coeff = 0.952H_0: r =0\\
H_1 :r\neq 0(Two tailed test)r difference = 0.952n=8Std error = \sqrt{\frac{1-r^2}{n-2} } =0.12496Test statistic t = 0.952/0.12496 = 7.618Alpha = 0.05df = 6p value = 0.000267This implies H0 is rejected.There exists a linear relation between the variables and r cannot be 00.952^2 = 0.906=90.6% of variation in weight can be explained by the linear relationship between weight and chest size