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Hypothesis Testing Finding the p-value and interpreting it. Pg 1.2: 4 assumptions

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Assumptions for Hypothesis Test of proportion: The normal population 1)Independence of events 2)Random sample or representative 3)Sample less than 10% 4)Success/Fail at least 10 each P Vocab: 2A Pg 1.3: when is p-val surprising?

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P-Values (a decimal number that is a probability) The P-Value is the probability of seeing data like these given that H o is true. H0H0 H a > H o HaHa What is the probability that we would see this sample come from the population of the Null Hypothesis Vocab: 7A Pg 1.4: when do you reject the Ho when do you accept the Ho

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H o and C.I. (paired together) If the H a falls in a C.I. based on your critical value than the H a is just the normal variableness of sampling. fail to reject the H o Samples vary – fail to reject the H o Can’t accept H o because other samples might fall outside the C.I. Vocab: 6A

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H o and C.I. (paired together) But if the H a falls outside a C.I. based on your critical value, than the H a replaces the H o as the population proportion until another sample comes along that says different. reject the H o This sample couldn’t have reasonably come from the population – reject the H o Vocab: 6A

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P-Values (a two tail test vs one tail) The smaller the p-value the less likely it was sample variableness 95% 5% Not Surprised Surprised ! 0.05

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P-Values (a two tail test vs one tail) 0.025 The smaller the p-value the less likely it was sample variableness 95% 2.5% Not Surprised Surprised ! 0.025 Pg 1.5: formula for z-score

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One-Proportion z-test (probability it came from the Null population) convert the z-score to a probability and you have your p-value

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Example #1 There are supposed to be 20% orange M&Ms. Suppose a bag of 122 has only 21 orange ones. Does this contradict the company's 20% claim? Assumptions:Hypothesis Statement: Null Hypothesis:Alternate Hypothesis: Critical value: P-value: Conclusion in context: Pg 2.2: z-score for sample proportion Pg 2.3: p-value for sample proportion Pg 2.4: based on p-val conclude

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Example #2 A 1996 report from the U.S. Consumer Product Safety Commission claimed that at least 90% of all American homes have at least one smoke detector. A city's fire department has been running a public safety campaign about smoke detectors consisting of posters, billboards, and ads on radio and TV and in the newspaper. The city wonders if this concerted effort has raised the local level above the 90% national rate. Building inspectors visit 400 randomly selected homes and find that 376 have smoke detectors. Find Assumptions:Hypothesis Statement: Null Hypothesis:Alternate Hypothesis: Critical value: P-value: Conclusion: Pg 3.2: z-score for sample proportion Pg 3.3: p-value for sample proportion Pg 3.4: based on p-val conclude

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