Question

use the hypothesis test for linear correlation flow chart interactive to answer the following question. sixty pairs of values result in a linear correlation coefficient of r=0.198. using a 0.05 significance level, the critical values for the hypothesis test are -0.254 and 0.254. which one of the following is the correct conclusion? choose the correct answer below. a. there is sufficient evidence to support the claim that there is no linear correlation. b. there is not sufficient evidence to support the claim of a linear correlation. c. there is sufficient evidence to support the claim of a linear correlation.

Explanation:

Step1: Recall Hypothesis Test Rule

For a linear correlation hypothesis test, we compare the correlation coefficient \( r \) with the critical values. If \( r \) is between the critical values (\(-\text{critical} < r < \text{critical}\)), we fail to reject the null hypothesis (which typically states there is no linear correlation). If \( r \) is outside (less than \(-\text{critical}\) or greater than \(\text{critical}\)), we reject the null hypothesis.

Step2: Compare \( r \) and Critical Values

Given \( r = 0.198 \), critical values are \(-0.254\) and \( 0.254 \). Since \(-0.254 < 0.198 < 0.254\), \( r \) lies between the critical values. This means we fail to reject the null hypothesis (no linear correlation), so there is not sufficient evidence to support the claim of a linear correlation.

Answer:

B. There is not sufficient evidence to support the claim of a linear correlation.