ECON10005 Lecture Notes - Lecture 13: Sampling Distribution, Null Hypothesis, Variance
27 Jul 2018
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Hypothesis test using the sampling distribution to test an assumption/hypothesis. Can use point/interval estimates to test assumptions about the unknown population parameter. In specifying a research hypothesis, we"re setting up a comparison. Decision rule that tells us how to use the data to decide between the null and the alternative hypothesis. Since the null forms the basis of comparison, all hypothesis tests begin by assuming the null is true. Decision rule specifies conditions under which we would rejet the null hypothesis in favour of the alternative. Use the sample mean as our data: is a realisation of the estimator (cid:3364) which is distributed as (,(cid:3097)(cid:3118)(cid:3041) ) If we assume the null is true, then: Note: for now assume that the variance of the parent distribution is known. The sampling distribution of (cid:3364) allows us to evaluate the likelihood of an observation given the null. If we observe a sample mean that"s extremely unlikely under the null, we reject it.
