s_m11_handouts

# s_m11_handouts - Rev F08 STA 2023 Module 11 Inferences for...

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Rev. F08 http://faculty.valenciacc.edu/ashaw/ 1 STA 2023 Module 11 Inferences for Two Population Means Rev.F08 2 Learning Objectives Upon completing this module, you should be able to: 1. Perform inferences based on independent simple random samples to compare the means of two populations when the population standard deviations are unknown but are assumed to be equal . 2. Perform inferences based on independent simple random samples to compare the means of two populations when the population standard deviations are unknown but are not assumed to be equal . ht p:/ faculty. valenciacc . edu/ashaw/ Click link to download other modules. Rev.F08 3 Two Population Means ht p:/ faculty. valenciacc . edu/ashaw/ Click link to download other modules. In the previous two modules, we learned how to obtain confidence intervals and perform hypothesis tests for one population mean . Sometimes, however, we might want to perform a hypothesis test to decide whether the mean price of single family homes at Orlando is greater than the mean price of single family homes at Cocoa ; or, we might want to find a confidence interval for the difference between the two mean prices . In this module, we are going to learn how to perform inferences for two populations means when the population standard deviations are unknown .

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Rev. F08 http://faculty.valenciacc.edu/ashaw/ 2 Rev.F08 4 Comparing Two Groups The natural display for comparing two groups is boxplots of the data for the two groups, placed side- by-side. For example: ht p:/ faculty. valenciacc . edu/ashaw/ Click link to download other modules. Rev.F08 5 Comparing Two Means Once we have examined the side-by- side boxplots , we can turn to the comparison of two means . The parameter of interest is the difference between the two means , μ 1 2 . ht p:/ faculty. valenciacc . edu/ashaw/ Click link to download other modules. Rev.F08 6 Comparing Two Means Remember that, for independent random quantities, variances add . So, the standard deviation of the difference between two sample means is We still don’t know the true standard deviations (population standard deviations) of the two groups, so we need to estimate and use the standard error . ( ) 2 2 1 2 1 2 1 2 SD y y n n ! " = + ( ) 2 2 1 2 1 2 1 2 s s SE y y n n ! = + ht p:/ faculty. valenciacc . edu/ashaw/ Click link to download other modules.
Rev. F08 http://faculty.valenciacc.edu/ashaw/ 3 Rev.F08 7 Comparing Two Means (Cont.) ht p:/ faculty. valenciacc . edu/ashaw/ Click link to download other modules. Rev.F08

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s_m11_handouts - Rev F08 STA 2023 Module 11 Inferences for...

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