Question

a pediatrician wants to determine the relation that may exist between a childs height and head circumference. she randomly selects 8 children from her practice, measures their height and head circumference, and obtains the data shown in the table. complete parts (a) through (e).

click here to see the table of critical values for correlation coefficient.

(c) compute the linear correlation coefficient between the height and head circumference of a child.
r = 0.668
(round to three decimal places as needed.)

(d) does a linear relation exist between height and head circumference? select the correct choice and fill in the answer box to complete your choice.
(round to three decimal places as needed.)

○ a. yes, the variables height and head circumference are positively associated because r is negative and the absolute value of the correlation coefficient is greater than the critical value, □.

○ b. no, the variables height and head circumference are not linearly related because r is negative and the absolute value of the correlation coefficient is less than the critical value, □.

○ c. yes, the variables height and head circumference are positively associated because r is positive and the absolute value of the correlation coefficient is greater than the critical value, □.

○ d. no, the variables height and head circumference are not linearly related because r is positive and the absolute value of the correlation coefficient is less than the critical value, □.

Explanation:

To determine if a linear relation exists, we check the sign of \(r\) (positive here) and compare \(|r|\) to the critical value. For \(n = 8\) (number of data - points), the critical value from the Table of Critical Values for Correlation Coefficient is \(0.707\). Since \(r=0.668\) is positive and \(|r| = 0.668<0.707\), we refer to the options.

Answer:

D. No, the variables height and head circumference are not linearly related because \(r\) is positive and the absolute value of the correlation coefficient is less than the critical value, \(0.707\)