inference articles
What fundamental role do Confidence Intervals (CIs) serve beyond summarizing findings with a point estimate?
What is the most frequently set level of confidence for estimation procedures?
What does stating 95% confidence primarily assert about the estimation procedure itself?
Which three main elements are required for the construction of a confidence interval?
Assuming constant sample size, how does increasing the desired confidence level affect the Margin of Error (MOE)?
How does a larger sample size generally impact the Standard Error and the resulting interval?
Which statement reflects a common, technically inaccurate interpretation of a single realized 95% CI?
If the 95% CI for the difference in conversion rates between two designs spans zero (e.g., -0.5% to +1.5%), what is the conclusion regarding the difference?
If the 95% CI for the difference in recovery times is (2.1 days to 4.5 days), what is the appropriate decision regarding a null hypothesis of zero difference?
Why is it mathematically impossible to construct a confidence interval that guarantees 100% coverage of the true population parameter?
What is the formal mathematical structure for adjusting understanding in light of new facts?
What does Bayesian refinement primarily involve regarding pre-existing knowledge?
What term quantifies the initial belief an individual or model holds before any new evidence arrives?
What does the likelihood function describe in terms of observed data (D) and a parameter state (θ)?
Which component of Bayesian inference represents the revised, updated belief about the parameter after incorporating new data?
The fundamental relationship in Bayes' Theorem states that the Posterior is proportional to which two components multiplied together?
What happens to the Posterior distribution calculated from one round of data when a subsequent round of data is analyzed?
If a prior chosen is very diffuse or flat, what largely dictates the shape of the resulting posterior belief?
In the formal expression $P(\theta|D) = \frac{P(D|\theta) P(\theta)}{P(D)}$, what is the function of $P(D)$?