BUS310_L15_3.8.11

# BUS310_L15_3.8.11 - Inferential Statistics Fundamentals of...

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Lecture 15: Inferential Statistics / Fundamentals of Hypothesis Testing I
Outline Review Chapter 8: Estimating Unknown Population Values (Confidence Intervals) à Example Review Chapter 9: Testing Hypotheses about Unknown Population Values One Numerical Variable – Testing Hypotheses about a Population Mean One-Tail Tests versus Two-Tail Tests PHStat, ‘One Sample Tests’, ‘t Test for the Mean, Sigma unknown’ One Categorical Variable – Testing Hypotheses about a Population Proportion PHStat, ‘One Sample Tests’, ‘Z Test for a Proportion’ Statement of Hypotheses (H0 and H1) The P-value Conclude H1 if (1 – P-value) > (1 – α) New Material: Chapter 10 – Hypothesis Testing with ANOVA (Analysis of Variance) Are the means of population one and two different? H1: μ1 ≠ μ2 H0: μ1 = μ2

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How are Chapters 9 and 10 Different? Review Chapter 9: Testing Hypotheses about Unknown Population Values Is the population mean different than 25? H1: μ ≠ 25 H0: μ = 25 Are the means of population one and two different? H1: μ1 ≠ μ2 H0: μ1 = μ2 1 numerical variable Add a categorical variable (e.g., gender, office 1 and 2, etc.), compare means of the numerical variable across categories
Data, Single Variable Tests of Hypotheses Chapter 9 Estimate Chapter 8 Numerical Categorical Population Mean Numerical Categorical Population Proportion Population Mean Population Proportion Inferential Statistics: 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 of all sales invoices per month is \$x . (support or reject the hypothesis based on sample statistics) Estimate proportion of sales invoices with errors (Confidence Interval : 95% confident that the proportion is between x and y (interval around the point estimate) Null Hypothesis that the proportion of sales invoices with errors is x

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Point and Interval Estimates Point estimate: value of the sample statistic, Confidence interval: a range of numbers constructed around the point estimate Probability is known that the population parameter is somewhere within Point Estimate Lower Confidence Limit Upper Confidence Limit Width of confidence interval
Problem 8.14 (page 252) The data in the file ‘MoviePrices’ contain the price for 2 tickets with online service charges, large popcorn, and 2 medium soft drinks at a sample of 6 theater chains (from Wall Street Journal). Construct a 95% Confidence Interval estimate for the

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BUS310_L15_3.8.11 - Inferential Statistics Fundamentals of...

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