Chapter13_STAT1100_LC.ppt", filename="Chapter13_STAT1100_LC.ppt", filename="Chap

# Chapter13_STAT1100_LC.ppt", filename="Chapter13_STAT1100_LC.ppt", filename="Chap

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Inference About Comparing Two Populations Statistics for Management and Economics Chapter 13

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Comparing Two Populations… Previously we looked at techniques to estimate and test parameters for one population: Population Mean μ , Population Variance σ 2 , and Population Proportion p We will still consider these parameters when we are looking at two populations , however our interest will now be: The difference between two means. The ratio of two variances. The difference between two proportions.
Difference of Two Means… In order to test and estimate the difference between two population means , we draw random samples from each of two populations. Initially, we will consider independent samples, that is, samples that are completely unrelated to one another. (Likewise, we consider for Population 2) Sample, size: n 1 Population 1 Parameters: Statistics:

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Difference of Two Means… In order to test and estimate the difference between two population means , we draw random samples from each of two populations. Initially, we will consider independent samples, that is, samples that are completely unrelated to one another. Because we are compare two population means, we use the statistic:
Sampling Distribution of 1. is normally distributed if the original populations are normal –or– approximately normal if the populations are nonnormal and the sample sizes are large (n 1 , n 2 > 30) 2. The expected value of is 3. The variance of is and the standard error is:

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Making Inferences About Since is normally distributed if the original populations are normal –or– approximately normal if the populations are nonnormal and the sample sizes are large (n 1 , n 2 > 30), then: is a standard normal (or approximately normal) random variable. We could use this to build test statistics or confidence interval estimators for
Making Inferences About …except that, in practice, the z statistic is rarely used since the population variances are unknown. Instead we use a t -statistic. We consider two cases for the unknown population variances: when we believe they are equal and conversely when they are not equal . ??

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When are variances equal? How do we know when the population variances are equal? Since the population variances are unknown, we can’t know for certain whether they’re equal, but we can examine the sample variances and informally judge their relative values to determine whether we can assume that the population variances are equal or not.
Equal Variances Test Statistic for Calculate – the pooled variance estimator as… …and use it here: degrees of freedom

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Equal Variances CI Estimator for The confidence interval estimator for when the population variances are equal is given by: degrees of freedom pooled variance estimator
Unequal Variances Test Statistic for The test statistic for when the population variances are unequal is given by: Likewise, the confidence interval estimator is: degrees of freedom

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Which case to use? Which case to use? Equal variance or unequal variance?
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## This note was uploaded on 06/25/2008 for the course BUSSPP MCE taught by Professor Atkins during the Spring '08 term at Pittsburgh.

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Chapter13_STAT1100_LC.ppt", filename="Chapter13_STAT1100_LC.ppt", filename="Chap

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