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Hypothesis Mean 1 Notes Spring

Hypothesis Mean 1 Notes Spring - 2 of 13 1.2 Testing a...

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2 of 13 1.2 Testing a claims when σ is known REVIEW What is a hypothesis test? A hypothesis test calculates the probability of observing our sample data as- suming the null hypotheses H 0 is true . If the probability is low enough ( p -value α ), we reject H 0 and have evidence to support our alternative hy- pothesis H a . Eight simple steps 0. Write down what is known . 1. Determine which type of hypothesis test to use. 2. Check the test’s requirements . 3. Formulate the hypothesis : H 0 , H a 4. Determine the significance level α . 5. Find the p -value . 6. Make the decision . 7. State the final conclusion . K-T-R-H-S-P-D-C: “Know The Right Hypothesis So People Don’t Com- plain” What is the p -value? The p -value represents the probability of observing our sample data assuming H 0 is true. We use the sampling distribution to determine if sampling error could explain our observed sample statistic’s deviation from H 0 ’s claim about the parameter. If we decide to reject H 0 , the p -value is the actual Type I error for the study data. 1 The p -value is calculated using the test statistic and it’s corresponding distribution. Common form of a test statistic test statistic = (sample statistic) - (null hypothesis of parameter) (standard deviation of sample statistic) (1) What are the types of errors? Type I error α / p -value occurs when we reject H 0 but H 0 is actually true . The p -value is the Type I error. (ex. Convicting a innocent person — when H 0 is innocence.) Type II error β occurs when we fail to reject H 0 but H 0 is actually false . (ex. Letting a criminal go free — when H 0 is innocence.) 1.2 Testing a claims when σ is known USE Often used to help answer: 1 The α we use to make our decision is just the maximum Type I error we will accept. It is the significance level, not the actual Type I error. Anthony Tanbakuchi MAT167
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Testing a claim about a population mean 3 of 13 1. Is the mean of a population equal to μ 0 ? 2. Is the mean of a population different than μ 0 ? COMPUTATION One sample hypothesis test, σ known. Definition 1.1 requirements (1) simple random sample, (2) σ known, (3) C.L.T.
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