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BUS310_L14_3.3.11

# BUS310_L14_3.3.11 - Inferential Statistics Fundamentals of...

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Lecture 14: Inferential Statistics / Fundamentals of Hypothesis Testing
Outline Chapter 8: Review 1. Estimating Unknown Population Values 2. Numerical Data: Confidence Interval for a Population Mean (‘PHStat’, ‘Confidence Intervals’, ‘Estimate for the Mean, Sigma unknown’, p.243 to 248) 3. Categorical Data: Confidence Interval for a Population Proportion (‘PHStat’, ‘Confidence Intervals’, ‘Estimate for the Proportion’) Chapter 9: Testing Hypotheses about Unknown Population Values 1. Recognizing the Problem Numerical Data – Tests Concerning Population Means Categorical Data – Tests Concerning the Population Proportion

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Outline Chapter 9: Testing Hypotheses about Unknown Population Values 2. Statement of Hypotheses Determine the question being asked. Population Mean bigger than 10? Set up 2 hypotheses: The Null Hypothesis always contains the equal sign (H0: µ < 10) The Alternative Hypothesis is the complement of the Null: H1: µ > 10 3. The P-value The p-value gives the probability of the sample results, if the null hypothesis were really true Use the P-value to decide whether to conclude H 0 or H 1 Calculate the actual confidence in alternative hypothesis: 1 – P-value Compare with Level of Significance ( α ) as a decision rule. If α = .05, you need to be at least 95% confident in the alternative hypothesis to conclude it.
Outline Chapter 9: Testing Hypotheses about Unknown Population Values 4. How to communicate the results of a hypothesis test using confidence in your alternative hypothesis: Assume α is .05 and P-value is .021. Required confidence in alternative is 1- .05 = .95 (or 95%). Actual confidence is 1 - .021 = .979 (or 97.9% ) Since our confidence of 97.9% exceeds the required confidence of 95%, we can conclude the alternative hypothesis. For the example: 97.9% confident that the population mean is larger than 10. Reject the Null Hypothesis at the 0.05 level of significance (or: at the 95% confidence level) 5. How to use PHStat to do the analysis for you

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Data, Single Variable Tests of Hypotheses Chapter 9 Estimate Chapter 8 Numerical Categorical Population Mean Numerical Categorical Population Proportion Population Mean Population Proportion Review: Inferential Statistics: Inductive Reasoning: Use specifics to make broader generalizations Inferential Statistics : Process of using sample results to estimate unknown population parameters like population mean and population proportion Point estimate Interval estimate H0: μ = x H1: μ ≠ x Estimate mean dollar amount of sales invoices per month (Confidence Interval : 95% confident that the \$ amount is between \$x and \$y (interval around the point estimate) Null Hypothesis that the mean dollar amount x for all customers has not changed from last year, or equals a certain amount. (support or reject the hypothesis based on sample stats) Estimate proportion of sales invoices with errors (Confidence Interval : 95% confident that the proportion is between x% and y% (interval around the point estimate)
Point and Interval Estimates Point estimate:

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