Comp233Online Lecture NotesHypothesis Testing

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COMP 233
Aug 13, 2023
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Page 2 of 29 DEF.: Hypothesis Testing; Hypothesis Testing is a Statistical test used to determine whether the hypothesis assumed for a random sample of data, stands true for the entire population. Simply, the hypothesis is an assumption which is tested to determine the relationship between two data sets (sample and population). In Hypothesis Testing, two opposing hypotheses about a population are formed: Null Hypothesis (H 0 ) and Alternative Hypothesis (H a ) . The Null Hypothesis is the statement which asserts there is no difference between the sample Statistic and population parameter; and is the one which is tested, while the Alternative Hypothesis is the statement which stands true if the Null Hypothesis is rejected. The following Hypothesis Testing Procedure is followed to test the assumption made: 1. Set up a Hypothesis Test: Formulate the Null, and Alternate Hypothesis. 2. Set a suitable Significance Level. 3. Determine a suitable Test Statistic. 4. Determine the Critical Region. 5. Perform computations. 6. Formulate a reject/accept Null Hypothesis decision.
Page 3 of 29 While testing the hypothesis, an individual may commit the following types of error: 1. Type-I Error: True Null Hypothesis is rejected, i.e. Null Hypothesis is rejected when it should be accepted. The probability of committing a type-I error is denoted by α , and is called the level of significance. If α = P[type- I error] = P[reject H 0 H 0 is true] then (1 α) = P[accept H 0 H 0 is true]. (1 α) corresponds to the concept of Confidence Interval . 2. Type-II Error: A False Null Hypothesis is accepted, i.e. Null Hypothesis is accepted when it should be rejected. The probability of committing a type-II error is denoted by β. If β = P[type- II error] = P[accept H 0 H 0 is false] then (1 β) = P[reject H o H 0 is false]. (1 β) is defined as the Power of a Statistical Test.
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