Which statement best describes the difference between a p-value and a confidence interval?

Which statement best describes the difference between a p-value and a confidence interval?

• A. A p-value is the probability that the null hypothesis is true.
• B. A p-value measures evidence against H0; a confidence interval provides a range for a parameter with a certain confidence level.
• C. A p-value and a confidence interval are the same thing.
• D. A confidence interval is only about the sample mean, not the parameter.

Answer: (B)

The main idea here is how p-values and confidence intervals convey different kinds of information from data. A p-value measures how surprising the observed data would be if the null hypothesis were true; it tells us about evidence against the null. It does not assign any probability to the null itself being true. A confidence interval, on the other hand, gives a range of values for the parameter that we would consider plausible given the data, with a specified confidence level (like 95%). It’s about estimating the parameter and expressing uncertainty around that estimate, not about testing a single hypothesis. So, the statement that best captures the distinction is that the p-value evaluates evidence against H0, while a confidence interval provides a plausible range for the parameter with a chosen confidence level. Why the other ideas don’t fit: a p-value is not the probability that the null is true; the two concepts are not the same thing; and a confidence interval is not limited to the sample mean—it can be formed for many parameters (differences, slopes, etc.), reflecting uncertainty about the true value rather than just a single data point.

The main idea here is how p-values and confidence intervals convey different kinds of information from data. A p-value measures how surprising the observed data would be if the null hypothesis were true; it tells us about evidence against the null. It does not assign any probability to the null itself being true.

A confidence interval, on the other hand, gives a range of values for the parameter that we would consider plausible given the data, with a specified confidence level (like 95%). It’s about estimating the parameter and expressing uncertainty around that estimate, not about testing a single hypothesis.

So, the statement that best captures the distinction is that the p-value evaluates evidence against H0, while a confidence interval provides a plausible range for the parameter with a chosen confidence level.

Why the other ideas don’t fit: a p-value is not the probability that the null is true; the two concepts are not the same thing; and a confidence interval is not limited to the sample mean—it can be formed for many parameters (differences, slopes, etc.), reflecting uncertainty about the true value rather than just a single data point.