If the confidence level is 95%, how is the p-value described according to the material?

If the confidence level is 95%, how is the p-value described according to the material?

• A. The p-value is the opposite of the confidence level.
• B. The p-value equals 95%.
• C. The p-value equals 5%.
• D. The p-value is independent of the confidence level.

Answer: (A)

The key idea is how confidence level and p-value relate through the alpha (significance) level. A 95% confidence level means we’re willing to accept a 5% chance of a wrong conclusion about the null, so the alpha is 0.05. The p-value is the observed probability of obtaining data as extreme as what was observed under the null hypothesis, and it corresponds to that remaining 5% tail region used to judge significance. In this sense, describing the p-value as the complement or opposite of the confidence level fits the material, because the 95% interval and the 5% tail become the two sides of the same decision framework. The other options don’t hold in general: the p-value is not simply 95%, nor necessarily exactly 5% unless the data yield that boundary, and the p-value is not independent of the confidence level since they are linked through the alpha threshold used for decision making.

The key idea is how confidence level and p-value relate through the alpha (significance) level. A 95% confidence level means we’re willing to accept a 5% chance of a wrong conclusion about the null, so the alpha is 0.05. The p-value is the observed probability of obtaining data as extreme as what was observed under the null hypothesis, and it corresponds to that remaining 5% tail region used to judge significance. In this sense, describing the p-value as the complement or opposite of the confidence level fits the material, because the 95% interval and the 5% tail become the two sides of the same decision framework. The other options don’t hold in general: the p-value is not simply 95%, nor necessarily exactly 5% unless the data yield that boundary, and the p-value is not independent of the confidence level since they are linked through the alpha threshold used for decision making.