 # Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. przesypkai4 2022-07-16 Answered
Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. $r=0.767,n=25$

a. Critical values: $r=±0.396$, no significant linear correlation
b. Critical values: $r=±0.487$ , no significant linear correlation
c. Critical values: $r=±0.396$ , significant linear correlation
d. Critical values: $r=±0.487$ , significant linear correlation
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Given:
$\gamma =0.767$
$n=25$
$\alpha =0.05$

The critical value $\gamma$ at $\alpha =0.05$ is $±0.396$
And the observed correlation value is $0.767$

The observed correlation value is greater than the critical value. Thus, there is a significant linear relationship occurs between the variables.
Hence, the correct option is (c)