## Elementary Statistics

Part 3: Inferential Statistics

#### Sections

• 8. Statistical Inference: Confidence Intervals (pdf)
• 9. Statistical Inference: Significance Tests about Hypotheses (pdf)
• 10. Comparing Two Groups (pdf)
• Review of Part 3 (pdf)

#### Interval estimates

• age of the universe (Rmd pdf)
• margin of error (Rmd pdf)
• confidence interval for a proportion (Rmd pdf)
• confidence interval for a mean (Rmd pdf)

#### Comparing two groups

• smoking then and now ... test for equality of two proportions (r pdf)
• cell phones while driving ... test for equality of two means (Rmd pdf)
• Etruscan and Italian skulls (Rmd pdf)
• Darwin's plants, 1876 ... paired data (Rmd pdf)

#### Data (for selected hw exercises)

• Chapter 8 (r)
• Chapter 9 (r)
• Chapter 10 (r)
• Part 3 (r)

#### R commands for Part 3

• arithmetic:
• +, -, *, /, ^

• mean and sd:
• mean(data)
• sd(data)

• normal and binomial probability distributions:
• pnorm(q, mean, sd), qnorm(p, mean, sd)
• dbinom(x, size, prob), pbinom(q, size, prob)

• confidence intervals:
• for proportion: x <- 12; n <- 25; prop.test(x, n); prop.test(x, n)\$conf.int[1:2]; prop.test(x, n, conf.level=0.99)
• for mean: data <- rnorm(25); t.test(data); t.test(data)\$conf.int[1:2]; t.test(data, conf.level=0.99)

#### Homework

• Chapter 8 -- 8.6 (nutrient), 8.17 (stem cells), 8.18 (z-score), 8.21 (fear), 8.23 (exit poll), 8.25 (simulation), 8.30 (anorexia), 8.31 (stock market), 8.45 (simulation), 8.49 (fail), 8.55 (tofu), 8.60 (bootstrap)
• Chapter 9 -- 9.2 (H_0 or H_a?), 9.4 (GPA), 9.14 (dogs), 9.18 (headache), 9.21 (garlic), 9.31 (work), 9.33 (pollution), 9.35 (asthma), 9.39 (anorexia), 9.49 (testing), 9.52 (misleading), 9.56 (selective reporting), 9.65 (errors)
• Chapter 10 -- 10.3 (drinking), 10.6 (aspirin), 10.8 (aspirin), 10.16 (housework), 10.25 (nicotine), 10.28 (survey), 10.36 (knees), 10.40 (teeth), 10.41 (fish), 10.49 (social), 10.59 (coffee), 10.67 (family size)

#### Review Exercises

Consolidate your understanding of the concepts in part 3 by working through a number of these exercises.

Review exercises and problems for part 3
• Chapter 8 -- 8.73 (nondrinkers), 8.82 (sad), 8.86 (eBay), 8.87 (income), 8.94 (doctor)
• Chapter 9 -- 9.57 (errors), 9.59 (sampling distributions), 9.68 (free-throws), 9.74 (hockey), 9.85 (tennis balls)
• Chapter 10 -- 10.70 (method), 10.76 (friends), 10.94 (tea), 10.99 (alcoholics), 10.108 (seat belts)
• Review of Part 3 -- R3.5 (services and taxes), R3.17 (evolution), R3.21 (buying), R3.22 (balances), R3.31 (math)

cparrish@sewanee.edu