Course review
Review each learning objective in this topic, then open its concept explanation or question set.
Learning objective
• 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.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• 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.
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Learning objective
• 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.
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Learning objective
• 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.
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Learning objective
• 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.
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Learning objective
• Use Poisson distribution, mean and variance. • Sum of independent Poisson variables is Poisson. • Choose between normal, binomial and Poisson models based on context.
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Learning objective
• 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.
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Learning objective
• 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.
Start with the concept explanation, then practise to create mastery evidence.