Week2B&3B2304 - ADM2304: One Proportion Dr. Suren...

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1 ADM2304: One Proportion Dr. Suren Phansalker 1. Hypothesis Testing: All Scientific methodologies depend on first using a hypothesis or or plausible explanation and then proving or disproving this hypothesis. In the Science of Statistics the Hypothesis Testing is a highly specialized methodology which is used for Accepting or Rejecting the Hypotheses for the Parameters of a Population. Remember, Hypothesis Testing is always done for Population Parameters, and different Statistic-s are used for Accepting or Rejecting the Hypotheses.
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2 So far, we have learnt about the Central Limit Theorem, CLT, for Means & Proportions, Confidence Intervals, CI, for Means & Proportions and Sample Size, n, when dealing with Proportions. It is now an appropriate time to consider Hypothesis Testing of Proportions. 2. Hypothesis Tests for One Proportion: Hypothesis Tests for all parameters come in three forms. Test #1: Two Tailed Tests Structure of this Test for One Proportion is as follows: H 0 : p = p 0 Î Null ( Notice ‘0’ in H 0 ) Hypothesis. H A : p p 0 Î Alternate ( Notice ‘A’ in H A ) Hypothesis. Here the assumed value is p 0 and it is a value which we want to disprove. The test is called “Two Tailed” because it is possible that p > p 0 or p < p 0 or p p 0 .
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3 If the Null Hypothesis, H 0 cannot be disproved then we say, Do Not Reject H 0 . If we can disprove the Null Hypothesis, then we say Reject H 0 . We rarely say Accept Alternate Hypothesis, H A . This is the typical statistical usage of expressions which can be called Statistical “jargon”. We also establish a formal methodology for performing Hypothesis Tests. An Example would demonstrate it clearly. 3. Example for Two Tailed Test for One Proportion: Remember, in the “Voting Fraud” example we did, n = 100, and Test the hypothesis that that the population proportion, p is equal to 0.80.
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Week2B&amp;amp;3B2304 - ADM2304: One Proportion Dr. Suren...

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