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Hypothesis testing for multiple parameters•Testing the difference among multiple proportions •Sampling distribution for multiple proportions (Chi-square)•Testing the difference among multiple means•Why a t-test is not used to compare multiple means?
EXAMPLEA manufacturer of stereo amplifiers has three assembly lines. We want to test whether the three lines do differ with respect to the number (proportion) of defectives produced. Independent samples of 30 amplifiers each are selected from the output of the lines, and the number of defectives is observed. The data are as follows:Conduct a test of the hypothesis given above at the 5% significance level.TESTING THE DIFFERENCE AMONG MULTIPLE PROPORTIONS
In this case, independent random samples are selected that result in binomially distributed random variables Y1, Y2, …, Yk where Yi is based on nitrials with success probability on each trialThe null and the alternative are as follows:What are the null and the alternative hypothesis for the example?