A confidence interval (and p-value) associated with a parameter (e.g., the mean, or a b in regression) assumes:
A)The residuals are normally distributed.
B)The sampling distribution of the parameter estimate is normal.
C)The data are normally distributed.
D)The data have heterogeneity of variance.

Question

Quizplus · Accepted Answer

Confidence intervals and p-values rely on the assumption that the sampling distribution of the parameter estimate is normal. This assumption is based on the central limit theorem, which states that when the sample size is large enough, the sampling distribution of the mean (or other parameter) will be approximately normal regardless of the distribution of the population. The other choices, such as normality of the residuals or data, or heterogeneity of variance, may affect the validity of other statistical tests (such as regression assumptions or ANOVA), but are not essential for the validity of the confidence interval or p-value.

A Confidence Interval (And P-Value) Associated with a Parameter (E