<p> Chapter 11- Testing A Claim</p><p>Key Vocabulary:</p><p>Null hypothesis Alternate hypothesis P-Value Statistical significance</p><p>1-sided 2-sided test statistic significance level Type I Type II</p><p>Power α β σ</p><p>Calculator Skills:</p><p> z-test z-interval</p><p>11.1 Significance Tests: The Basics (pages 684-704) 1. What is a null hypothesis? A statement being tested. (The status quo statement, it suggests no change or no difference.)</p><p>Notated as Ho.</p><p>2. What is an alternative hypothesis? The claim about a population that we are trying to find evidence for. (Statement that suggests that something has changed or is different than expected.) Notated as Ha.</p><p>3. What conditions should be satisfied before significance testing? SRS, Normality, Independence</p><p>4. In statistics, what is meant by the p-value ? The probability that the observed outcome would take a value as extreme as or more extreme than that actually observed. 5. If a p-value is small, what do we conclude about the null hypothesis ?</p><p>There is more evidence against the null hypothesis, Ho. A low p-value means the observed result is unlikely to occur by chance if the null hypothesis, Ho, is true. 6. If a p-value is large, what do we conclude about the null hypothesis ?</p><p>It means there is not enough evidence against the null hypothesis, Ho,. There is no reason not to believe the null hypothesis. 7. How small should the p-value be in order to claim that a result is statistically significant? The p-value needs to be as small as or smaller than the alpha, α, level. The alpha level depends on our significance level. </p><p>8. What does statistically significant mean? This means that something, an event, is unlikely to happen by chance. </p><p>11.2 Carrying Out Significance Tests (pages 704-716) 1. Explain the difference between a one-sided alternative hypothesis and a two-sided alternative hypothesis? One sided means a specific direction such as greater than or less than. A two-sided alternative means either direction, greater than or less than. 1-sided < or > 2 sided ≠ 2. Write the steps to follow for significance testing. </p><p>11.3 Use and Abuse of Tests ( pages 716-722) 1. What does a test statistic estimate? The degree of evidence provided by a sample against the null hypothesis, Ho.</p><p>2. What is meant by a significance level ? The level that is “good enough” to be believed. 95% significance level means 5% of not being true.</p><p>3. Significance tests are not always valid. What are some factors that can invalidate a test?</p><p> Faulty data collection</p><p> Outliers in the data</p><p> Testing a hypothesis after sampling (using results to meet your needs/wants)  Testing a sample that is too small 11,4 Using Inference to Make Decisions (pages 722-739) 1. Explain the difference between a Type I error and a Type II error.</p><p>Type 1: If you reject Ho, when the Ho is actually true.</p><p>Type 2: If you fail to reject Ho , when Ho is false.</p><p>2. What is the relationship between the significance level α and the probability of a Type I error? The significance level, α ( alpha), of any fixed level test is the probability of a Type 1 error. </p><p>Alpha, α, is the probability that the test will reject the Ho, when in fact the Ho is true.</p><p>3. Describe how to calculate the Power of a significance test?</p><p>Power: the probability that a fixed level, α, significance test will reject Ho , when a particular alternative value of the parameter is true, is called power.</p><p>The power of a test against any alternative is 1 minus the probability of a Type 2 error, β. (1 – β) </p><p>4. How can the Power of a test be increased? Which of the methods are the most feasible?</p><p> Increase α – A test at a 5% significance level will have a greater chance of rejecting the alternative than a 1% test because the strength of evidence required is less.</p><p> Increase sample size – More data will provide more information about x , so we have a better chance of distinguishing values of µ.</p><p> Decrease σ – the smaller the deviation the more precise our estimate </p>