Math 1025 - Lesson Plan Chapter 7v2 - Chapter 7 Hypothesis...

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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 one-tailed or two-tailed statistical test and find a p -value 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 0 read “H subzero” or “H naught.” {H 0 contains equal sign}. Alternative hypothesis A statement of inequality such as >, , or <. Must be true if H 0 is false. Denoted H a read “H sub-a.” H 0 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 0 : μ≥k H 0 : μk H 0 : 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 0 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%.
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a. Identify the verbal claim and write it as a mathematical statement. b. Write the complement of the claim. c. Identify H 0 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 0 OR (2) Fail to reject H 0 Since hypothesis testing is based on Sample data, there is always a chance of making the wrong decision. Actual Truth about H 0 Decision H 0 is True H 0 is False Fail to Reject H 0 Correct Decision Type II Error Reject H 0 Type I Error Correct Decision Type I Error - If H 0 is Rejected when it is TRUE.
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