ECON10005 Lecture Notes - Lecture 16: Confidence Interval, Random Variable, Null Hypothesis
27 Jul 2018
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Where v = k = n-1 degrees of freedom. We start from the sampling distribution; if we assumed (cid:2870) is known we have: Firstly, define a symmetric interval associated with an area of ( )% under the standard normal density function: In order to define a (1 )% confidence interval we need to rearrange the above interval so it"s centered around the unknown . Represent an interval that"s associated with an area of ( )% under the density function: To derive the confidence interval, rearrange the above interval so it"s centered solely around the unknown parameter (cid:2870): Therefore, a confidence interval for (cid:2870) is given by: Note: to find (cid:2870) values look at the table. Begin by specifying a null hypothesis, remembering that this forms the basis for comparison: Depending on the research question, the alternative can take one of three forms: The sampling distribution of the estimator is a (cid:2870) random variable with k=n-1 degrees of freedom.
