When are results considered significant in this test?

When are results considered significant in this test?

• A. The results are significant if the calculated value is higher than the critical value.
• B. The results are significant if the p-value is less than 0.05.
• C. The results are significant if the calculated value equals two times the critical value.
• D. The results are significant if the calculated value is equal to or lower than the critical value.

Answer: (D)

Significance in a hypothesis test is judged by how unlikely the observed result would be if the null hypothesis were true, which we quantify using a p-value against a chosen alpha level (often 0.05). The key idea is that if the p-value is equal to or below this threshold, the result is considered statistically significant, because it would occur by chance only a small, preselected amount of the time. In this context, the calculated value refers to the p-value, and the critical value is the alpha level; when p ≤ alpha, we reject the null. That’s why using the inclusive criterion of equal to or lower than the critical value is the best match.

Significance in a hypothesis test is judged by how unlikely the observed result would be if the null hypothesis were true, which we quantify using a p-value against a chosen alpha level (often 0.05). The key idea is that if the p-value is equal to or below this threshold, the result is considered statistically significant, because it would occur by chance only a small, preselected amount of the time. In this context, the calculated value refers to the p-value, and the critical value is the alpha level; when p ≤ alpha, we reject the null. That’s why using the inclusive criterion of equal to or lower than the critical value is the best match.