Question

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 alphaequals​0.05, 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?

Answer 1

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 = 0.952

H_0: r =0\\

H_1 :r\neq 0

(Two tailed test)

r difference = 0.952

n=8

Std error = \sqrt{\frac{1-r^2}{n-2} } =0.12496

Test statistic t = 0.952/0.12496 = 7.618

Alpha = 0.05

df = 6

p value = 0.000267

This implies H0 is rejected.

There exists a linear relation between the variables and r cannot be 0

0.952^2 = 0.906=90.6% of variation in weight can be explained by the linear relationship between weight and chest​ size