Question

Suppose that, instead of the critical value approach, you decided to use the p-value approach and found that the p-value for the test in this problem is equal to 0.0368. This p-value is best interpreted as the following:

a) Strong evidence against the null hypothesis
b) Weak evidence against the null hypothesis
c) Strong evidence in favor of the null hypothesis
d) Weak evidence in favor of the null hypothesis

Answer 1

The p-value of 0.0368 indicates a 3.68% probability of the observed result occurring by chance under the null hypothesis, and since it is less than the common alpha level of 0.05, it is considered strong evidence against the null hypothesis.

Step-by-step explanation:

The p-value represents the probability of observing a sample outcome as extreme as, or more extreme than, the one observed, given that the null hypothesis is true. A p-value of 0.0368 suggests that there is a 3.68% chance of obtaining a test result this extreme assuming the null hypothesis is correct. Comparing this to a conventional alpha level (significance level) of 0.05 (5%), which is a common threshold for rejecting the null hypothesis, we find the p-value is less than 0.05. Therefore, this provides strong evidence against the null hypothesis, and typically one would reject the null hypothesis in favor of the alternative hypothesis.