When testing whether the correlation coefficient differs from zero, the value of the test statistic is t₂₀ = 1.95 with a corresponding p-value of 0.0653. At the 5% significance level, can you conclude that the correlation coefficient differs from zero? A) Yes, since the p-value exceeds 0.05. B) Yes, since the test statistic value of 1.95 exceeds 0.05. C) No, since the p-value exceeds 0.05. D) No, since the test statistic value of 1.95 exceeds 0.05.

Question

Quizplus · Accepted Answer

The correct interpretation of a p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. In this case, the p-value is 0.0653, which means there is a 6.53% chance of obtaining a test statistic as large as 1.95 or larger if the correlation coefficient is actually zero. Since this p-value exceeds the significance level of 0.05, we fail to reject the null hypothesis and do not have sufficient evidence to conclude that the correlation coefficient differs from zero. Therefore, the correct answer is choice C. Choice B is incorrect because the test statistic value should be compared to a critical value, not 0.05, and there is no critical value given in the question.

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