Assumptions of Theorem  Conclusions 1. Y normal 2: Simple 3: Null about (model random hypothesis Sampling assumption) samples true (not a Distribution (Distribution of ) (model model assumption) assumption)  1: Normal 2: Mean µ0 3: Standard deviation  Corresponds to third column in table on the previous page Note that the model assumption that the sample is a simple (in particular, that the Yi’s as defined earlier are random sample independent) is used to prove: that the sampling distribution is normal and (even more importantly) that the standard deviation of the sampling distribution is . This illustrates a general phenomenon that independence conditions are usually important in deriving the variance formulas usually taught in applied statistics courses. Consequences of model assumptions:
Assumptions of Theorem  Conclusions about Sampling Distribution (Distribution of )  1. Y normal (model assumption) 2: Simple random samples (model assumption) 3: Null hypothesis true (not a model assumption) 1: Normal 2: Mean µ0 3: Standard deviation  Corresponds to third column in table on the previous page Note that the model assumption that the sample is a simple random sample (in particular, that the Yi’s as defined earlier are independent) is used to prove: that the sampling distribution is normal and (even more importantly) that the standard deviation of the sampling distribution is . This illustrates a general phenomenon that independence conditions are usually important in deriving the variance formulas usually taught in applied statistics courses. Consequences of model assumptions:
WorkshopSlidesDayTwo2017-part1.docx