According to the material, which statement describes the relationship between p-value and confidence level?

According to the material, which statement describes the relationship between p-value and confidence level?

• A. They are independent.
• B. They are the same as the confidence level.
• C. The p-value is the square of the confidence level.
• D. The p-value is the opposite of the confidence level.

Answer: (D)

The main idea is how p-values and confidence levels connect through a common threshold. The p-value measures how compatible your data are with the null hypothesis—it’s the probability of seeing data as extreme or more extreme if the null is true. The confidence level, on the other hand, is about how often an interval method would capture the true parameter if you repeated the study many times. The link between them comes from the significance level, alpha, which equals 1 minus the confidence level. In practice, you decide a confidence level (for example, 95%), which fixes alpha at 0.05. Then you look at the p-value from your test: if the p-value is at most alpha, you reject the null. If the p-value is larger than alpha, you do not reject. So the p-value and the confidence level aren’t opposites or the same thing; they’re tied together by the threshold alpha that governs both hypothesis tests and confidence intervals. For a 95% level, a p-value of 0.05 or smaller leads to rejection, and the corresponding 95% confidence interval would exclude the null value.

The main idea is how p-values and confidence levels connect through a common threshold. The p-value measures how compatible your data are with the null hypothesis—it’s the probability of seeing data as extreme or more extreme if the null is true. The confidence level, on the other hand, is about how often an interval method would capture the true parameter if you repeated the study many times.

The link between them comes from the significance level, alpha, which equals 1 minus the confidence level. In practice, you decide a confidence level (for example, 95%), which fixes alpha at 0.05. Then you look at the p-value from your test: if the p-value is at most alpha, you reject the null. If the p-value is larger than alpha, you do not reject.

So the p-value and the confidence level aren’t opposites or the same thing; they’re tied together by the threshold alpha that governs both hypothesis tests and confidence intervals. For a 95% level, a p-value of 0.05 or smaller leads to rejection, and the corresponding 95% confidence interval would exclude the null value.