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Unformatted text preview: Chapter 7  Hypothesis Testing with One Sample Section 7.1  Introduction to Hypothesis Testing Objectives • State a null hypothesis and an alternative hypothesis • Identify type I and type I errors and interpret the level of significance • Determine whether to use a onetailed or twotailed statistical test and find a pvalue • Make and interpret a decision based on the results of a statistical test • Write a claim for a hypothesis test Hypothesis test A process that uses sample statistics to test a claim about the value of a population parameter. Statistical hypothesis A statement, or claim, about a population parameter. • Need a pair of hypotheses: * one that represents the claim * the other, its complement When one of these hypotheses is false, the other must be true . Null hypothesis • A statistical hypothesis that contains a statement of equality such as ≤ , =, or ≥ . • Denoted H read “H subzero” or “H naught.” {H contains equal sign}. Alternative hypothesis • A statement of inequality such as >, ≠ , or <. • Must be true if H is false. • Denoted H a read “H suba.” H and H a are complementary Statements. Stating a Hypothesis • To write the null and alternative hypotheses, translate the claim made about the population parameter from a verbal statement to a mathematical statement. • Then write its complement. • Always assume μ =k and then look at the sampling distribution based on this assumption. • 3 ways to state Hypothesis: H : μ≥k H : μk H : μ=k H a : μ<k H a : μ>k H a : μ≠k Try It Yourself 1  (p. 366) Write the claim as a mathematical sentence. State H and H a , and identify which represents the claim. (1) A consumer analyst reports that the mean life of a certain type of automobile battery is not 74 months. (2) A television manufacturer publishes that the variance of the life of a certain type of television is less than or equal to 3.5. #26. p. 376 {A research organization reports that 28% of the residents in Ann Arbor, MI are college students.} (3) A radio station publicizes that its proportion of the local listening audience is greater than 39%. a. Identify the verbal claim and write it as a mathematical statement. b. Write the complement of the claim. c. Identify H and H a and determine which one represents the claim. Types of Errors • No matter which hypothesis represents the claim, always begin the hypothesis test assuming that the equality condition in the null hypothesis is true. • At the end of the hypothesis testing, you make 1 of 2 Decisions about the null hypothesis: (1) Reject H OR (2) Fail to reject H • Since hypothesis testing is based on Sample data, there is always a chance of making the wrong decision....
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This note was uploaded on 02/07/2012 for the course MATH 1025 taught by Professor Raney during the Fall '10 term at Metro State.
 Fall '10
 Raney
 Math, Statistics

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