Which statement best describes the interpretation of P-values and a 95% confidence interval (CI) when the CI includes the null value?

Which statement best describes the interpretation of P-values and a 95% confidence interval (CI) when the CI includes the null value?

• A. P-values quantify the probability that the null hypothesis is true.
• B. P-values provide the exact probability that the observed result occurred by chance.
• C. If the 95% CI includes the null, the result is not statistically significant at the 0.05 level.
• D. A 95% CI indicates the probability that the true parameter lies within the interval.

Answer: (C)

Interpreting P-values and a 95% confidence interval hinges on where the null value sits relative to the interval and what each statistic represents. When the 95% CI includes the null value, it means the data do not provide enough evidence to reject the null hypothesis at the conventional 0.05 level. In practical terms, the corresponding p-value would be greater than 0.05, so we do not reach statistical significance at that threshold. Keep in mind what the p-value and the CI are actually telling you. A p-value is the probability, assuming the null hypothesis is true, of obtaining results as extreme or more extreme than what was observed. It is not the probability that the null hypothesis is true. A 95% CI is a range of plausible values for the true parameter based on the data; it reflects the precision of the estimate and the long-run performance of the method, not a single probability statement about this specific interval being the true parameter. If the null value lies inside this interval, you cannot claim a statistically significant effect at the 0.05 level. So, when the CI includes the null, the result is not statistically significant at the 0.05 level.

Interpreting P-values and a 95% confidence interval hinges on where the null value sits relative to the interval and what each statistic represents. When the 95% CI includes the null value, it means the data do not provide enough evidence to reject the null hypothesis at the conventional 0.05 level. In practical terms, the corresponding p-value would be greater than 0.05, so we do not reach statistical significance at that threshold.

Keep in mind what the p-value and the CI are actually telling you. A p-value is the probability, assuming the null hypothesis is true, of obtaining results as extreme or more extreme than what was observed. It is not the probability that the null hypothesis is true. A 95% CI is a range of plausible values for the true parameter based on the data; it reflects the precision of the estimate and the long-run performance of the method, not a single probability statement about this specific interval being the true parameter. If the null value lies inside this interval, you cannot claim a statistically significant effect at the 0.05 level.

So, when the CI includes the null, the result is not statistically significant at the 0.05 level.