In hypothesis testing, which statement best distinguishes a p-value from a confidence interval?

In hypothesis testing, which statement best distinguishes a p-value from a confidence interval?

• A. P-value tests alternative hypothesis; CI ignores null value.
• B. P-value tests null hypothesis; CI provides range of plausible values for the parameter and indicates precision; if CI excludes the null value, p<0.05.
• C. P-value measures effect size; CI provides range of precision.
• D. P-value and CI convey identical information.

Answer: (B)

The main distinction is that the p-value and a confidence interval address different questions about the data. The p-value asks, under the assumption that the null hypothesis is true, how likely is the observed result or something more extreme? A small p-value means the observed effect is unlikely if the null is true, providing evidence against the null. A confidence interval, on the other hand, gives a range of values for the true parameter that are compatible with the data at a chosen confidence level and shows how precise the estimate is. It tells you the plausible size of the effect and how much uncertainty surrounds it. There’s a useful connection: if the null value lies outside the confidence interval (for a two-sided test), the p-value is typically below the significance level (e.g., p < 0.05). If the null value is inside the interval, the p-value tends to be above the significance level. For example, a 95% CI that excludes zero indicates a p-value less than 0.05.

The main distinction is that the p-value and a confidence interval address different questions about the data. The p-value asks, under the assumption that the null hypothesis is true, how likely is the observed result or something more extreme? A small p-value means the observed effect is unlikely if the null is true, providing evidence against the null.

A confidence interval, on the other hand, gives a range of values for the true parameter that are compatible with the data at a chosen confidence level and shows how precise the estimate is. It tells you the plausible size of the effect and how much uncertainty surrounds it.

There’s a useful connection: if the null value lies outside the confidence interval (for a two-sided test), the p-value is typically below the significance level (e.g., p < 0.05). If the null value is inside the interval, the p-value tends to be above the significance level. For example, a 95% CI that excludes zero indicates a p-value less than 0.05.