In Step 4, how is significance determined?

In Step 4, how is significance determined?

• A. Compare the calculated value to the critical value; it must be less than the p-value threshold.
• B. Compare the calculated value to the standard deviation.
• C. Compare the calculated value to the mean difference.
• D. The calculated value is compared to the critical value; the calculated value needs to be equal to or less than the critical value.

Answer: (D)

At this stage, significance is decided by whether the observed test statistic falls into the rejection region defined by the critical value. The critical value marks the cutoff from the null distribution at the chosen alpha level. For a left-tailed test, the rejection region lies at values less than or equal to that cutoff, so if the calculated statistic is equal to or smaller than the critical value, it is deemed significant. This is the direct decision rule you apply in Step 4. This approach focuses on how extreme the result is under the null hypothesis, not on the standard deviation or the mean difference alone. The comparison to the critical value (and the resulting conclusion about significance) is what tells you whether to reject the null. In other test setups, you’d compare the absolute statistic to a critical value for a two-tailed test, but the underlying idea remains: you decide significance by whether the statistic falls into the defined extreme region.

At this stage, significance is decided by whether the observed test statistic falls into the rejection region defined by the critical value. The critical value marks the cutoff from the null distribution at the chosen alpha level. For a left-tailed test, the rejection region lies at values less than or equal to that cutoff, so if the calculated statistic is equal to or smaller than the critical value, it is deemed significant. This is the direct decision rule you apply in Step 4.

This approach focuses on how extreme the result is under the null hypothesis, not on the standard deviation or the mean difference alone. The comparison to the critical value (and the resulting conclusion about significance) is what tells you whether to reject the null. In other test setups, you’d compare the absolute statistic to a critical value for a two-tailed test, but the underlying idea remains: you decide significance by whether the statistic falls into the defined extreme region.