Given the linear correlation coefficient r and the sample size n, determine the

Question

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 = 0.523, n = 25 Critical values: r = ±0.487, significant linear correlation Critical values: r = ±0.396, no significant linear correlation Critical values: r = ±0.396, significant linear correlation Critical values: r = ±0.487, no significant linear correlation

Explanation / Answer

Here we have to test,

H0 : Rho = 0 Vs H1 : Rho not= 0

where Rho is population correlation between he two variables.

Assume alpha = level of significance = 0.05

Given that,

r = 0.523

n = 25

Critical value for n = 25 with n-2 = 25-2 = 23 degrees of freedom is 0.396.

There are two critical values +0.396 and -0.396 since the test is two tailed.

Here r > critical value

Reject H0 at 5% level of significance.

Conclusion : There is sufficient evidence to say that there is relationship between two variables.

significant linear correlation Critical values: r = ±0.396

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