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Understanding Population Mean and Proportion Significance Tests

This chapter addresses the application of significance tests in statistics, focusing on tests for population means and proportions. It emphasizes that the assumption of Simple Random Sampling (SRS) is crucial for valid results, especially with larger sample sizes. For small samples (n < 15), t-procedures are applicable only if the data is approximately Normal. For larger samples (n > 30), these procedures remain robust even with skewed distributions. Additionally, it outlines the process for conducting a one-proportion z-test, including required conditions for Normality.

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Understanding Population Mean and Proportion Significance Tests

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  1. Chapter 12 Significance Tests in Practice

  2. Section 12.1 – Population Mean Tests

  3. Section 12.1 – Population Mean Tests

  4. Section 12.1 – Population Mean Tests

  5. Section 12.1 – Population Mean Tests • Using the t Procedures [Recall]: • Except in the case of small samples, the assumption that the data are an SRS from the population of interest is more important that the assumption that the population distribution is Normal • n < 15: use t procedures if the data are close to Normal. If the data are clearly not Normal, or if outliers are present, do not use t procedures. • n > 15: use t procedures except in the presence of outliers or strong skewness • Large samples [n > 30]: use t procedures even for clearly skewed distributions

  6. Section 12.2 – Population Proportion Tests • Remember the formula for a confidence interval for proportions. • When performing a significance test, we will calculate standard error using the value for p specified in the null hypothesis.

  7. Section 12.2 – Population Proportion Tests • One proportion z-test • *Remember the Normality condition* • n*p0 • n*(1 - p0) • H0: p = p0 • Ha: p ≠ p0 or > p0 or < p0

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