Question

use the hypothesis test for linear correlation flow chart interactive to answer the following question. forty pairs of values result in a linear correlation coefficient of r = -0.444. using a 0.05 significance level, the critical values for the hypothesis test are -0.312 and 0.312. which one of the following is the correct conclusion? choose the correct answer below. a. there is sufficient evidence to reject the claim of a linear correlation. b. there is sufficient evidence to support the claim of a linear correlation. c. there is not sufficient evidence to reject the claim of a linear correlation. d. there is not sufficient evidence to support the claim of a linear correlation.

Explanation:

Step1: Compare r with critical values

The linear correlation coefficient \( r = -0.444 \), and the critical values are \( -0.312 \) and \( 0.312 \). We check if \( r \) is outside the range of the critical values. Since \( -0.444 < -0.312 \), \( r \) is in the rejection region.

Step2: Determine the conclusion

In hypothesis testing for linear correlation, if \( |r| \) is greater than the positive critical value (or \( r \) is less than the negative critical value), we reject the null hypothesis (which typically claims no linear correlation) and conclude there is sufficient evidence to support the claim of a linear correlation. Here, \( r = -0.444 \) is less than \( -0.312 \), so we reject the null hypothesis, meaning there is sufficient evidence to support the claim of a linear correlation.

Answer:

B. There is sufficient evidence to support the claim of a linear correlation.