What you’ll learn8 learning objectivesChoose one objective for a focused lesson, or study the complete topic.—AHL 4.12 (HL)—Data collection and validity• Design valid surveys/questionnaires and choose relevant variables/data.• Use unbiased, structured and precise questioning.• Categorize numerical data for chi-square tests with suitable degrees of freedom.• Distinguish reliability and validity; know test-retest, parallel forms, content and criterion-related validity.Syllabus objective—AHL 4.13 (HL)—Non-linear regression• Use technology for least-squares regression curves: linear, quadratic, cubic, exponential, power and sine.• Use residual sum of squares and coefficient of determination R^2 to evaluate fit.• Know R^2 alone is not enough to choose a model.Syllabus objective—AHL 4.14 (HL)—Random variable transformations• Use linear transformations of random variables: E(aX+b)=aE(X)+b and Var(aX+b)=a^2Var(X).• Use expected value and variance for linear combinations of independent random variables.• Use sample mean and unbiased sample variance as estimators.Syllabus objective—AHL 4.15 (HL)—Sampling distributions and CLT• Linear combinations of independent normal random variables are normal.• Use distribution of sample mean: Xbar ~ N(mu, sigma^2/n) for normal populations.• Use central limit theorem; n>30 is sufficient in examinations.Syllabus objective—AHL 4.16 (HL)—Confidence intervals• Construct confidence intervals for the mean of a normal population.• Use normal distribution when sigma is known and t-distribution when sigma is unknown.• Interpret confidence intervals in context.Syllabus objective—AHL 4.17 (HL)—Poisson distribution• Use Poisson distribution, mean and variance.• Sum of independent Poisson variables is Poisson.• Choose between normal, binomial and Poisson models based on context.Syllabus objective—AHL 4.18 (HL)—Advanced hypothesis testing• Use critical values and critical regions.• Test population means with normal or t distributions, including paired/unpaired samples.• Test proportions with binomial distribution and population means with Poisson distribution.• Test whether population correlation rho is zero; know Type I and II errors and their probabilities.Syllabus objective—AHL 4.19 (HL)—Transition matrices and Markov chains• Use transition matrices, powers and state matrices: s_n=T^n s_0.• Use transition diagrams for discrete dynamical systems.• Work with regular Markov chains, steady state and long-term probabilities.• Recognize steady state as eigenvector for eigenvalue 1.Syllabus objective