# Elementary Statistics: Chapter 8 Notes

**Topics:**Statistical hypothesis testing, Normal distribution, Sample size

**Pages:**13 (3594 words)

**Published:**April 27, 2013

* Chapters 2 and 3 used “descriptive statistics when summarizing data using tools (such as graphs), and statistics (such as mean and standard deviation) * Methods of inferential statistics use sample data to make an inference or conclusion about a population * Two main activities of inferential statistics are using sample data to… * Estimate a population parameters

* Such as estimating a population parameter with a confidence interval * Test a hypothesis or claim about a population parameter * Chapter 7 presented methods for estimating a population parameter with a confidence intervals * This chapter presents the method of hypothesis testing

* A hypothesis is a claim or statement about a property of a population * A hypothesis test (or test of significance) is a procedure for testing a claim about a property of a population * Main objective of this chapter is to develop the ability to conduct hypothesis tests for claim made about a population proportion “p”, a population mean “μ”, or a population standard deviation “σ” * Formal method of hypothesis testing uses several standard terms and conditions in a systemic procedure * CAUTION: When conducting hypothesis tests instead of jumping directly to procedures and calculations, be sure to consider context of data, source of data, and sampling method used to obtain sample data

Section 2: Basics of Hypothesis Testing

* This section presents individual components of a hypothesis test * Part 1 discusses basic concepts of hypothesis testing

* Know and understand following:

* How to identify null hypothesis and alternative hypothesis from a given claim, and how to express both in symbolic form * How to calculate value of test statistic, given a claim and sample data * How to identify critical value(s), given a significance level * How to identify P-value, given a value of test statistic * How to state conclusion about a claim in simple and nontechnical terms * Part 2 discusses power of hypothesis test

Part 1: Basic Concepts of Hypothesis Testing

* Methods presented in this chapter are based on rare event rule (Section 4-1) * If, under a given assumption, probability of a particular observed event is extremely small, we conclude that assumption is probably not correct * Following this rule, test a claim by analyzing sample data in an attempt to distinguish between results that can easily occur by chance and results that are highly unlikely to occur by chance * Can explain occurrence of highly unlikely results by saying that either a rare event indeed occurred or that underlying assumption is not correct

Working with Stated Claim: Null and Alternative Hypothesis

* Null Hypothesis (H0) is a statement that value of a population parameter (such as proportion, mean, or standard deviation) is equal to some claimed value * Term null is used to indicate no change or effect or no difference * Test a null hypothesis directly by assuming (or pretending) it is true and reach a conclusion to either reject or fail to reject it * Typical null hypothesis = 0.5

* Alternative Hypothesis (H1, Ha, or HA) is statement that parameter has a value that somehow differs from null hypothesis * Symbolic form of alternative hypothesis must use one of these symbols , ≠ * It is rare, but symbols are occasionally used in hypothesis H0 * Conduct hypothesis test by assuming that proportion, mean, or standard deviation is equal to some specific value so that we can work with a single distribution having a specific value * If conducting a study and want to use a hypothesis test to support claim, claim must be worded so that it become alternative hypothesis and can be expressed using only symbols , or ≠ * Can never support a claim that some parameter is equal to some specific value * Start = Identify specific claim...

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