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CHAPTER 10: STATISTICAL INFERENCE: ONE-SAMPLE HYPOTHESIS TEST 10.1: Introduction to Hypothesis Testing Using statistical inference Covering classical statistical inference which is from Ronald A. Fisher, Jerzy Neyman, and Egon Pearson 2 topics: 1. Null hypothesis significance testing, 2. Confidence interval estimation New sampling distribution: t distribution New test statistic: t statistic…using it to test a hypothesis about the mean of a population Scientific Hypotheses Scientific method: 1. Observe nature, 2. Ask questions, 3. Formulate hypotheses, 4. Conduct experiments, 5. Develop theories and laws. 3 rd characteristic from above: formulate hypotheses Scientific hypothesis – a testable supposition that is tentatively adopted to account for certain facts and to guide in the investigation of others. It is a statement about nature that requires verification. Intelligent informed guesses about phenomena of interest; can be stated in the if-then form; truth or falsity can be determined by observation and experimentation Many hypotheses are not scientific hypotheses because they are not testable by experience…we do not have any way to currently test them Why Statistical Inference? When impossible to observe the entire population When a scientific hypothesis cannot be evaluated directly by observing all of the elements of a population, we might be able to use statistical inference to evaluate the hypothesis indirectly by observing a sample from the population of interest. Statistical Hypotheses
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Stated in general terms at the beginning Statistical hypothesis – statement about 1 or more parameters of a population distribution that requires verification Ex: is a new method more efficient than the old method? Null hypothesis – H 0 ; the one that we are testing; set up to be opposite of what the researcher believes to be true Alternative hypothesis – H 1 ; set up so that it corresponds to the researcher’s scientific hypothesis Hypothesis testing – process of choosing between the 2 hypotheses The 2 hypotheses are mutually exclusive and exhaustive The sample statistics from the experiment are used to estimate the unknown population parameters Hypothesis Testing and the Method of Indirect Proof Indirect proof method – listing all possible answers or solutions to a problem and showing that all but 1 are contrary to known fact or lead to an absurdity; by the process of elimination, we find a contradiction to all but 1
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