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11.1-11.2 Quiz MONDAY 3-3-14 Ch. 11 Test TUESDAY 3-11-14 HW-pgs. 698-699 (11.8-11.9, 11.12) www.westex.org HS, Teacher Website 2-25-14 Warm up—AP STATS Flip your penny ten times and keep track of how many tails you get. Put your result in the appropriate blank below. p = __________________________________ Ho: p = ____ Ha: p ≠ ____ (_____________) Brenden ___ Anisha ___ Heather ___ Kyle R. ___ Nick B. ___ Sal ___ ^ p = _____ Ali ___ Courtney ___ Rachel ___ Lisa ___ Nick T. ___ Bethany ___ Anderson ___ Geena ___ Kyle B. ___ Michael ___ Shannon ___ Theresa ___ z = ____________ P(Z< ___ or Z> ___) = 2P(Z< ___) = 2(___) = ____ Name_____________________________ Date____________ AP Statistics Section 11.1 Significance Tests: The Basics Objectives: Identify the three conditions that need to be present before doing a significance test for a mean. Explain what is meant by a test statistic and give its general form. Define p-value. Before performing a ____________________ __________ about a population mean or proportion the same three conditions must be verified as when we were getting ready to construct a _______. As in the previous chapter, the details for checking the ____________________ condition are different for __________ and ____________________: For means: population distribution Normal or __________ _______________ __________ ( For proportions: ) ____________________ and _________________________ Think back to yesterday when we talked about the paramedics’ response time on calls. We should confirm that the three important conditions are met. SRS ____________________________________________________________________ Normality ____________________________________________________________________ ____________________________________________________________________ Independence ____________________________________________________________________ **All three conditions are met, so we can proceed to the calculations.** A significance test uses data in the form of a __________ ____________________. Here are some principles that apply to most tests: The test is based on a statistic that ____________________ the value of the ___________________ as stated in the null hypothesis with an ____________________ of the parameter from the sample data. Values of the estimate __________ from the parameter value in the direction specified by the __________________ ________________ give evidence against ______. To assess how far the estimate is from the parameter, ____________________ the estimate. In many common situations, the test statistic has the form: In our paramedic example our test statistic is: where μo is the value of μ specified by the null hypothesis. The test statistic z says how _ __________ x is from μo in standard deviation units. Because the sample result is over two standard deviations below the hypothesize mean 6.7, it gives __________ ____________________ that the mean response time this year is not 6.7 minutes, but rather, less than 6.7 minutes. The null hypothesis ______ states the claim we are seeking evidence _______________. The test statistic measures how much the sample data diverge from the null hypothesis. If the test statistic is __________ and is in the ____________________ suggested by the alternative hypothesis ______, we have data that would be unlikely if ______ were true. We make “unlikely” precise by calculating a ________________, called a _____________. The P-value is simply the probability, computed assuming that ______ is true, that the observed outcome would take a value as extreme as or more extreme than that actually observed. The _______________ the P-value is, the _______________ the evidence _______________ Ho provided by the data. Small P-values are evidence against ______ because they say that the observed result is _______________ to occur when Ho is true. Large P-values __________ to give evidence against Ho. **See the examples below. Pay particular attention to what happens when Ha is two sided. The probability of the observed value being z units below or above the mean is twice what it would be if it was one sided because we are considering the chance of it falling in both tails!**