When testing whether the correlation coefficient differs from zero, the value of the test statistic is t₂₀ = −2.95 with a corresponding p-value of 0.0061. At the 5% significance level, can you conclude that the correlation coefficient differs from zero? A) Yes, since the p-value is less than 0.05. B) Yes, since the absolute value of the test statistic exceeds 0.05. C) No, since the p-value is less than 0.05. D) No, since the absolute value of the test statistic exceeds 0.05.

Question

Quizplus · Accepted Answer

The p-value of 0.0061 is less than 0.05, indicating that the probability of obtaining a test statistic as extreme or more extreme than the observed one under the null hypothesis is very low. Therefore, we reject the null hypothesis and conclude that the correlation coefficient differs from zero at the 5% significance level. Alternatively, choice B is incorrect because 0.05 is not a threshold for the absolute value of the test statistic; it is a threshold for the p-value. Choices C and D are incorrect because they state the opposite of what is true.

When Testing Whether the Correlation Coefficient Differs from Zero, the Value