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=0.543, n=25

a. Critical values: r = ±0.396, no significant linear correlation
b. Critical values: r = ±0.396, significant linear correlation
c. Critical values: r = ±0.487, significant linear correlation
d. Critical values: r = ±0.487, no significant linear correlation

Answer 1

a. Critical values : r = ±0.396, no significant linear correlation.

Explanation:

The critical value is 0.396 and test statistic is 0.543. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value Test statistics is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. In the given case test statistics value is greater than critical value then we should accept the null hypothesis.