Question

for a data set of brain volumes (cm³) and iq scores of four males, the linear correlation coefficient is r = 0.989. 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 (type integers or decimals. do not round. use a comma to separate answers as needed.) table of critical values of r number of pairs of data n critical value of r 4 0.950 5 0.878 6 0.811 7 0.754 8 0.707 9 0.666 10 0.632 11 0.602 12 0.576

Explanation:

Step1: Identify number of data - pairs

The number of male data - pairs (brain volumes and IQ scores) is $n = 4$.

Step2: Find critical values from the table

Looking at the table of critical values of $r$ for $n = 4$, the critical value is $0.950$. Since the correlation can be positive or negative, the critical values are $- 0.950,0.950$.

Step3: Compare the linear correlation coefficient with critical values

The given linear correlation coefficient is $r = 0.989$. Since $0.989>0.950$, it lies outside the range of $-0.950$ to $0.950$.

Answer:

$-0.950,0.950$; There is a significant linear correlation because the absolute value of the linear correlation coefficient $|r| = 0.989$ is greater than the critical value of $0.950$.