Section 7.6 Summary and final remarks
Subsection 7.6.1 Summary of scenarios
The scenarios studied in this chapter — sample proportion, sample mean, and difference in proportions or means — are not the only cases where sampling distributions arise. For example, the slope coefficient in linear regression also has a sampling distribution, which we study in Chapter 10. A summary table of sampling scenarios, including the sample statistic, the population parameter, the expected value, and the standard error formula, provides a useful reference for all the cases studied in this chapter.
Across all cases, the three key results remain the same:
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The expected value of the sample statistic equals the population parameter.
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The standard error decreases as the sample size increases.
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For large enough samples, the sampling distribution is approximately normal (CLT).
Subsection 7.6.2 Additional resources
An R script file of all R code used in this chapter is available here.
Subsection 7.6.3 What’s to come?
The upcoming Chapter 8 on confidence intervals will delve deeper into statistical inference. We will explore how to construct and interpret confidence intervals, what a confidence level means, the limitations of confidence intervals, and practical applications. The concepts of sampling distributions and standard errors developed in this chapter form the theoretical foundation for all of that work.
