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Unformatted text preview: Section 6.2 Tests of Significance Section 6.2 1 Statistical Inference • Confidence intervals are one of the two commonly used tools in statistical inference. • Confidence intervals are especially useful when the goal is to estimate a population parameter and include information about the precision of the estimate. • A second goal in statistical inference is to assess the evidence provided by the data in favor of some claim about the population. Section 6.2 2 Significance Tests • A significance test is a formal procedure for comparing observed data with a hypothesis about the population. The plausibility of the hypothesis is evaluated against the information provided by the data. • The hypothesis statement is always about the population parameters and always consists of two components: • Null hypothesis • Alternative hypothesis • The results of the test are often expressed in terms of a probability that describes how well the data matches the hypothesis. Section 6.2 3 Example - Ink Cartridges • The black ink cartridges for a particular type of inkjet printer have a labeled volume of 10 mL of ink. The manufacturing company periodically tests its filling machine for accuracy. A recent test of 100 ink fills had a mean volume of 9.971 mL. We will assume that the standard deviation of all ink fills is 0.2 mL. Section 6.2 4 Ink Inference • In this case, we are especially interested in knowing something specific about the population mean ink volume μ . • Does μ = 10 mL as labeled? • This is an ideal setting for a significance test. We want to investigate if the sample provides evidence that the labeled volume is incorrect. • The labeled volume will serve as our null hypothesis . • How likely is a sample mean of 9.971 mL if the true population mean is 10 mL? Section 6.2 5 General Test Procedure The general procedure for a significance test consists of five steps. 1. Specify a level of significance α . 2. State the null hypothesis and the alternative hypothesis. 3. Calculate the test statistic. 4. Find the p-value. 5. State the conclusion in the context of the problem. Section 6.2 6 Goal of Significance Testing • In significance testing, or hypothesis testing, we examine observed data for evidence against the null hypothesis. • The “evidence” is expressed as a probability of observing the sample result, assuming that the null hypothesis is true . • If the probability is small, then there is substantial evidence against the null hypothesis. Section 6.2 7 Stating Hypotheses We will skip step 1 for now and move to step 2. 1. Specify a level of significance α . 2. State the null hypothesis and the alternative hypothesis. 3. Calculate the test statistic....
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This note was uploaded on 04/02/2008 for the course STAT 226 taught by Professor Abbey during the Spring '08 term at Iowa State.
- Spring '08