Testing the Variance-ECO6416 - H a The variation is more...

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Testing the Variance: Is the Quality that Good? Suppose a population has a normal distribution. The manager is to test a specific claim made about the quality of the population by way of testing its variance σ 2 . Among three possible scenarios, the interesting case is in testing the following null hypothesis based on a set of n random sample observations: H 0 : Variation is about the claimed value.
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Unformatted text preview: H a : The variation is more than what is claimed, indicating the quality is much lower than expected. Upon computing the estimated variance S 2 based on n observations, then the statistic: χ ½ = [(n-1)S 2 ] / σ 2 has a Chi-square distribution with degree of freedom ν = n - 1. This statistic is then used for testing the above null hypothesis....
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