Question

When can you legitimately draw a cause-and-effect conclusion from a randomized experiment?

A) When the p-value is small
B) Always, no matter what the p-value is
C) Never, no matter what the p-value is
D) When the p-value is large

Answer 1

A cause-and-effect conclusion from a randomized experiment can be drawn when the p-value is small, particularly less than the alpha level (such as 0.05), as it suggests that the null hypothesis is unlikely and should be rejected.

Step-by-step explanation:

You can legitimately draw a cause-and-effect conclusion from a randomized experiment when the p-value is small. Specifically, this occurs when the p-value is less than the alpha level (often set at 0.05 or 5 percent), because it indicates that the observed results are very unlikely under the assumption that the null hypothesis is true. In such a case, you would reject the null hypothesis, suggesting a possible causation by whatever intervention or variable you are testing.

In practice, it's essential to compare the p-value to a predetermined significance level (α). If the p-value is less than α, you reject the null hypothesis. For example, with an α of 0.05:

• If the p-value < 0.05, reject the null hypothesis.
• If the p-value ≥ 0.05, do not reject the null hypothesis.

The correct answer to the question is A) When the p-value is small. A small p-value suggests that the event observed is a rare event under the null hypothesis, providing stronger evidence against the null hypothesis.