Let X1,...,Xn be a random sample from the exponential distribution with unknown parameter . Let 0 < 0 < 1 be two possible values of the parameter. Suppose that we wish to test the following hypotheses: H0: = 0, H1:

Calculating Probability and Drawing Inference using Central Limit Theorem for mean: - Ex1. Determining whether the mean lifetime claimed by a light bulb company is true in reality (refer to lecture 19 for a thorough example) - Statistical significance is when an effect in a study is real, and not likely to be due to random variation alone - Scheme of statistical inference (similar to proof by contradiction): o Initial claim/presumption o Observe (conduct study) and model (a distribution assuming claim) o Calculate probability (likeliness of observation if claim were true) o