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section 11.1 notes 0809.notebook March 14, 2012 Chapter 11 - Testing a Claim Section 11.1 Significance Tests: The Basics A significance test is a formal procedure for comparing observed data with a hypothesis whose truth we want to assess. Ex. 11.2 Call the paramedics!!!! Vehicle accidents can result in serious injuries to drivers and passengers. When they do, someone usually calls 911. Police, firefighters, and paramedics respond to these emergency calls as quickly as possible. Slow response times can have serious consequences for accident victims. In case of life-threatening injuries, victims generally need attention within 8 minutes of the crash. Several cities have begun to monitor paramedic response times. In one such city, the mean response time to all accidents involving life-threatening injuries last year was μ = 6.7 minutes with a standard deviation of σ = 2 minutes. The city manager shares this information with emergency personnel and encourages them to "do better" next year. At the end of the following year, the city manager selects a SRS of 400 calls involving life-threatening injuries and examines the response times. For this sample, the mean response time was x = 6.48 minutes. Do these data provide good evidence that response times have decreased since last year? section 11.1 notes 0809.notebook assess assess Ex: Null and Alternate for Call the Paramedics!!!!! March 14, 2012 section 11.1 notes 0809.notebook March 14, 2012 Cautions about Hypothesis Writing: 1) They are about parameters not statistics 2) Your alternate must be decided BEFORE you collect and analyze your data!! Conditions for a Hypothesis Test: Same as conditions for confidence intervals Ex: Conditions for Call a Paramedic!!! SRS: Normal: Independence: Test Statistic: t or z depending on what you are testing and the information you have Ex: Call the paramedics!!!!! P-value : Ex: Call the paramedics!!!! section 11.1 notes 0809.notebook March 14, 2012 Example: Does the job satisfaction of assembly workers differ when their work is machine-paced rather than self-paced? One study chose 18 subjects at random from a group of people who assembled electronic devices. Half of the subjects were assigned at random to each of two groups. Both groups did similar assembly work, but one work setup allowed workers to pace themselves, and the other featured an assembly line that moved at fixed time intervals so that the workers were paced by machine. The difference in job satisfaction scores follow a Normal distribution with standard deviation σ = 60. If there is no difference in job satisfaction between the two work environments, the mean is μ = 0. This is H0. The alternate says simple "there is a difference," Ha:μ≠0. Data from 18 workers gave x = 17. section 11.1 notes 0809.notebook March 14, 2012 Significance Level: the decisive P-value for which we will reject the null hypothesis *the significance level must be set before you do your calculations so extreme a result Is the "call a paramedic data" statistically significant? Interpreting your Results: A. The three C's: conclusion, connection, context Your conclusion should have a clear connection to your calculations and should be stated in the context of the problem. B. Reject the null or fail to reject the null. This is based on whether or not the data is statistically significant. Reject if data is statistically significant Fail to reject if data is not statistically significant Ex: Interpretation of the "Call a Paramedic" problem: section 11.1 notes 0809.notebook March 14, 2012 t