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Unformatted text preview: Hypothesis Testing Hypotheses- The null hypothesis – H : parameter = value- The alternative hypothesis – H a : parameter = value we would accept if we reject the null hypothesis ***All hypotheses must be written using the parameter symbol (p, μ , μ 1- μ 2 , μ d , β 1 , μ 1 = μ 2 = μ 3 ) except for the Chi Square tests AND the alternative hypothesis for ANOVA. Plan- Check the conditions.- Specify the model you will use to test the null hypothesis.- Specify the parameter of interest . Mechanics- Calculate a test statistic from the data.- Obtain a P-value = the probability that the observed value of the test statistic (or a more extreme value) could occur if the null model were correct.- If the P-value is small enough, we will reject the null hypothesis. Conclusion A Statistical conclusion: state the reason you have decided reject or fail to reject the null hypothesis. B Conclusion in context: write a complete, clear statement explaining what you conclude. Example – One Sample T Test A cell mobile manufacturer claims that its batteries last for 150 hours before needing to be recharged. A random sample of mobile phones was taken and the mean battery life was 142 hours before needing to be recharged. Does this indicate that the mean battery life is less than 150 hours? H : μ = 150 hours, H a : μ < 150 hours, P-value is 0.023 A Since p is small we reject the null hypothesis. B There is sufficient evidence to conclude that the mean battery life for this manufacturer is less than 150 hours. *** If you are asked to interpret the P-Value you would say: If the null hypothesis were true and the true mean battery life was 150 hours, there is a 2.3% chance of observing the results in our sample. 9c5214562af90156415caca8a24b6e6c6282a068.doc 1 H = the null hypothesis H a = the alternate hypothesis = the probability of a Type I error α = the probability of a Type II error β H TRUE H FALSE Do not reject H correct decision Type II error Reject H Type I error correct decision Confidence Intervals Confidence Interval A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, in our case, mean, proportion…; the estimated range being calculated from a given set of sample data. *** Remember, the confidence interval concerns the population parameter…thus, you create the confidence interval around the observed sample mean, proportion......
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This note was uploaded on 05/20/2008 for the course STAT 50 taught by Professor Weinstein during the Spring '08 term at Harvard.
- Spring '08