BUS310_L18_3.17.11 - Inferential Statistics / Hypothesis...

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Lecture 18: Inferential Statistics / Hypothesis Testing III Chapter 11 (Chi-Square Tests)
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Outline Review Chapter 10: Hypothesis Testing with ANOVA: Compare means among 2 categories: Compare means among 3 or more categories: Are the means of three or more populations different? H1: Not all μj are equal H0: μ1 = μ2 = … = μc (the c population means are equal) Which means are different / better? & Tukey-Kramer Procedure Are the means of population one and two different? H1: μ1 ≠ μ2 (the two population means are not equal) H0: μ1 = μ2 (the two population means are equal) Which mean is better? & look up in descriptive statistics
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New Material: Chapter 11 – Two categorical Variables: Testing for Equal Proportions 1. Both categorical variables have 2 categories: A 2X2 crosstab table a) Use approach in section 11-1. Use an existing table or create one with PHStat, ‘Descriptive Stats’, ‘Two-Way Tables and Charts’ b) Hypotheses: H0: π1 = π2 (the 2 populations have equal proportions/percents) H1: π1 ≠ π2 (the 2 populations have unequal proportions/percents) a) Obtain P-value from PHStat, ‘Two-Sample Tests’, ‘Chi Square Test for Differences in Proportions’ (Copy and paste your data into the worksheet created by PHStat) b) Conclusion: state your confidence in the alternative hypothesis , decide which hypothesis to conclude. 2. One categorical variable has c (>2) categories and one has 2 categories. a) Use approach in section 11-2. Use an existing table or create one with PHStat, ‘Descriptive Stats’, ‘Two-Way Tables and Charts’ b) Hypotheses: H0: π1 = π2 = … = πc (the c populations have equal proportions/percents) H1: Not all πj are equal ( the c population proportions are not all equal) a) Obtain P-value from PHStat, ‘Multiple-Sample Tests’, ‘Chi Square Test’ (Copy and paste your data into the worksheet created by PHStat). Make sure your table is a 2 X C table and not a C X 2 table.
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Example with 5 groups: ‘BEER.xls’ 1. Run an ANOVA to get the p-value. We are almost 100% confident that there are differences among the mean prices for the 5 beer types in the population (e.g., beers available in the US), based on our samples.
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Tukey-Kramer: Where are Differences in the Population? ‘BEER.xls’ The population mean of Type 2 (Craft Ale) is higher than that of 1 (Craft Lager), 4 (Regular), 5 (Low Calorie) (meaning: Craft Ale is typically more expensive in these other types) Type 3 (Import) is typically more expensive than 4 (Regular) and 5 (Low Calorie) Type 1 (Craft Lager) is typically more expensive than 4 (Regular) 1. Tukey Kramer Test shows you which population means are different , with 95% confidence 2. If you want to know which population means are higher , look at the sample means: 4: Regular $4.50 $5.50 $6.50 $7.50 5: Low Calorie 1: Craft Lager 3: Import 2: Craft Ale 3. Combine the 2 sources of information for your conclusion: According to the Tukey Kramer Test, we can be 95% confident that:
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Example: Different Tests for the Population of Shidler Students Collect data for a sample of 30 Shidler students: GPA Numerical Gender
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BUS310_L18_3.17.11 - Inferential Statistics / Hypothesis...

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