EC285 Chapter Notes - Chapter 12: Confidence Interval, Unimodality
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The student"s t-models form a family of related distributions that depend on a parameter known as degrees of freedom, df. Models are unimodal, symmetric, and bell-shaped but models with a few degrees of freedom have narrower peaks and have fatter tails than the normal model. Whenever you use s (sample standard deviation) to estimate , use t. For means, the right value for degrees of freedom is df = n 1. When certain conditions are met, the standardized sample mean, (cid:1872)=(cid:1877) (cid:4666)(cid:1877) (cid:4667) Confidence interval for the population mean, : (cid:1877) (cid:1872) 1 (cid:4666)(cid:1877) (cid:4667) Table z is used for each degrees of freedom value with confidence levels 80%, 90%, 95% Nearly normal condition: the data come from a distribution that is unimodal and symmetric. For small sample (n < 15 or so), the data should follow a normal model closely.
