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7.1 Introduction to Hypothesis Testing Key Concepts: –Hypothesis Tests –Type I and Type II Errors –Probability Value (or P-value) of a Test –Decision Rules

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7.1 Introduction to Hypothesis Testing Consider the following scenario: A fluorescent lamp manufacturer guarantees that the mean life of a certain type of lamp is at least 10,000 hours. You want to test this guarantee. To do so, you record the life of a random sample of 32 fluorescent lamps (see below). At α = 0.09, do you have enough evidence to reject the manufacturers claim? (#40 p. 384) 8,8009,15513,00110,25010,00211,4138,23410,402 10,016 8,015 6,110 11,005 11,555 9,254 6,991 12,006 10,420 8,302 8,151 10,980 10,186 10,003 8,814 11,445 6,277 8,632 7,265 10,584 9,397 11,987 7,556 10,380

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7.1 Introduction to Hypothesis Testing How can we test such claims? –Start with a pair of statistical hypotheses or statements about a population parameter. Null Hypothesis H o –Statistical hypothesis that contains a statement of equality like, =, or. Alternative Hypothesis H a –The complement of the null hypothesis. It is a statement that must be true of the null hypothesis if false. Practice forming H o and H a. #12 p. 367 #16

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7.1 Introduction to Hypothesis Testing When we conduct hypothesis tests, we always work under the assumption that the null hypothesis is true. We will reject H o only when there is enough evidence to do so. –We need to be aware of two types of errors that may occur in a study: A type I error occurs if a true null hypothesis is rejected. A type II error occurs if a false null hypothesis is not rejected. –Practice Identifying Errors #32 p. 368 (Flow Rate)

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7.1 Introduction to Hypothesis Testing Definitions and Symbols we will need later: –The probability of making a type I error is known as the significance level of the test and is denoted by α. –The probability of making a type II error is denoted by β.

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7.1 Introduction to Hypothesis Testing Once we have identified H o, H a, and α, we need to calculate the value of a test statistic and then use it to make a decision about H o. –Once way to make that decision is to use the probability value or P-value of the test. P-value = the probability of obtaining a sample statistic with a value as extreme as or more extreme than the one determined from the sample data. –The way we calculate the P-vale of a test depends on the type of test we are working with (left-tailed, right- tailed, or two-tailed). See page 362. Practice identifying the type of test #38 p. 368 (Clocks) #40 p. 368 (Lung Cancer)

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7.1 Introduction to Hypothesis Testing How do we decide whether or not to reject the null hypothesis? –We use decision rules based on the P-value: If the P-value of the test is less than or equal to the significance level, we reject H o. If the P-value of the test is greater than the significance level, we do not reject H o. Note: If we do not reject the null hypothesis, it doesnt mean we are saying H o is true. We are saying we do not have enough evidence to reject H o. #46 p. 369 (Gas Mileage)

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