Chapter 1: Introduction to Statistical Inference
- Defines statistical inference and explains its purpose.
- Introduces the concepts of population, sample, and sampling distribution.
- Real example: Estimating the average lifespan of a certain species of animal based on a sample of observed lifespans.
Chapter 2: Fundamentals of Sampling
- Covers random sampling, non-random sampling, and sampling bias.
- Explains how to select appropriate sample sizes.
- Real example: Determining the sample size needed to estimate the average height of students in a university with an acceptable level of accuracy.
Chapter 3: Estimation and Confidence Intervals
- Discusses the principles of estimation and introduces confidence intervals.
- Explains how to construct confidence intervals for population means, proportions, and other parameters.
- Real example: Estimating the proportion of people who support a political candidate based on a survey sample and constructing a confidence interval for this proportion.
Chapter 4: Hypothesis Testing
- Explains the concept of hypothesis testing, including the null hypothesis and alternative hypothesis.
- Introduces the p-value and its interpretation.
- Real example: Testing the hypothesis that two different manufacturing processes produce products with equal average weights based on experimental data.
Chapter 5: Tests of Significance for Means
- Focuses on hypothesis testing for population means.
- Covers t-tests, z-tests, and the central limit theorem.
- Real example: Testing the hypothesis that the average test score for a particular standardized exam is different for two groups of students.
Chapter 6: Tests of Significance for Proportions
- Covers hypothesis testing for population proportions.
- Explains the concepts of sample proportion, binomial distribution, and normal approximation.
- Real example: Testing the hypothesis that the proportion of households in a certain neighborhood that own a pet is greater than 50% based on a sample survey.
Chapter 7: Tests of Significance for Variances
- Explains the concept of variance and its significance in hypothesis testing.
- Introduces the F-test for testing the equality of two population variances.
- Real example: Testing the hypothesis that the variance of the weights of manufactured parts produced by two machines is the same.
Chapter 8: Nonparametric Tests
- Discusses nonparametric tests that do not require assumptions about the underlying distribution of data.
- Covers the Mann-Whitney U test, Kruskal-Wallis test, and chi-square test for independence.
- Real example: Testing the hypothesis that the distribution of incomes for two different occupations is the same using the Mann-Whitney U test.
