Question

for a data set of brain volumes (cm³) and iq scores of nine males, the linear correlation coefficient is r=0.647. use the table available below to find the critical values of r. based on a comparison of the linear correlation coefficient r and the critical values, what do you conclude about a linear correlation? click the icon to view the table of critical values of r. the critical values are -0.666,0.666. (type integers or decimals. do not round. use a comma to separate answers as needed.) since the correlation coefficient r is dropdown, there dropdown sufficient evidence

Explanation:

Step1: Determine n

The number of males (data pairs) \( n = 9 \).

Step2: Find critical values

From the table, for \( n = 9 \), the critical values of \( r \) are \( \pm 0.666 \) (since correlation can be positive or negative, we consider both bounds).

Step3: Compare r and critical values

The given \( r = 0.647 \). We check if \( |r| \) is greater than the positive critical value (or less than the negative, but here \( r \) is positive). \( 0.647 < 0.666 \), so \( r \) is between \( - 0.666 \) and \( 0.666 \).

Step4: Conclusion on linear correlation

If \( |r| \) is less than the critical value, we fail to reject the null hypothesis (of no linear correlation), meaning there is not sufficient evidence to support a linear correlation.

Answer:

Since the correlation coefficient \( r = 0.647 \) is between \( -0.666 \) and \( 0.666 \) (or \( 0.647 < 0.666 \) and \( 0.647 > - 0.666 \)), there is not sufficient evidence to support a linear correlation between brain volumes and IQ scores.

For the blanks:
First blank: between \( -0.666 \) and \( 0.666 \) (or \( 0.647 < 0.666 \) and \( 0.647 > - 0.666 \), or more succinctly "not in the rejection region" or "between the critical values")
Second blank: is not

(If we follow the dropdown logic, first blank: "between -0.666 and 0.666" (or "less than 0.666 and greater than -0.666"), second blank: "is not" (to indicate no sufficient evidence))