Section 10.7 Conclusion
Subsection 10.7.1 Summary of statistical inference
We’ve finished the last two scenarios, which we re-display in Table 10.7.1.
| Scenario | Population parameter | Notation | Point estimate | Symbol(s) |
|---|---|---|---|---|
| 1 | Population proportion | \(p\) | Sample proportion | \(\hat{p}\) |
| 2 | Population mean | \(\mu\) | Sample mean | \(\bar{x}\) or \(\hat{\mu}\) |
| 3 | Difference in population proportions | \(p_1 - p_2\) | Difference in sample proportions | \(\hat{p}_1 - \hat{p}_2\) |
| 4 | Difference in population means | \(\mu_1 - \mu_2\) | Difference in sample means | \(\bar{x}_1 - \bar{x}_2\) or \(\hat{\mu}_1 - \hat{\mu}_2\) |
| 5 | Population regression slope | \(\beta_1\) | Fitted regression slope | \(b_1\) or \(\hat{\beta}_1\) |
Armed with the regression modeling techniques you learned in Chapter 5 and Chapter 6, your understanding of sampling for inference in Chapter 7, and the tools for statistical inference like confidence intervals and hypothesis tests in Chapter 8 and Chapter 9, you’re now equipped to study the significance of relationships between variables in a wide array of data! Many of the ideas presented here can be extended into multiple regression and other more advanced modeling techniques.
Subsection 10.7.2 Additional resources
An R script file of all R code used in this chapter is available here.
Subsection 10.7.3 What’s to come
You’ve now concluded the last major part of this book on statistical inference with
infer. The closing Chapter 11 concludes this book with various short case studies involving real data, such as house prices in the city of Seattle, Washington in the US. You’ll see how the principles in this book can help you become a great storyteller with data!
