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AFM 113 — Analytic Methods for Business 2

Statistics the way the paper examines it — tables, a cheat sheet, and R output you can read — 89 lessons

The whole of AFM 113 as its hand-computed midterm and cumulative final examine it: how the paper is marked and the conventions the course fixes (the cumulative z-table, the t-table both ways, bracketed p-values, the four-step test), data and study design, describing one variable, correlation and the least-squares line, probability, discrete random variables, the normal distribution, the sampling distribution and the CLT, confidence intervals, hypothesis tests, two-sample and paired inference with the hand rule for Welch's df shown beside R's, proportions, inference for regression on the same eight-client dataset, and a cumulative rehearsal. Every computed quantity is graded on the number with the table lookup shown after you commit; every formula is checked by runnable Python; every line of R output came from a real run.

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How This Course Is Examined

27 cards
  1. The paper and the four-step mark 8 min ◈ 3
  2. The cheat sheet organised by parameter 8 min ◈ 5
  3. Reading the cumulative z-table 10 min ◈ 7
  4. Reading the t-table and bracketing a tail 10 min ◈ 5
  5. R is read, not written 9 min ◈ 7

Data, Sampling, and Study Design

40 cards
  1. Population, sample, parameter, statistic 9 min ◈ 6
  2. Target population, study population, and bias 9 min ◈ 5
  3. Probability sampling designs 10 min ◈ 6
  4. Non-probability designs and sampling error 8 min ◈ 5
  5. Variables and their roles 7 min ◈ 5
  6. Observational studies, experiments, and confounding 10 min ◈ 5
  7. R as a calculator 8 min ◈ 8

Describing One Variable

42 cards
  1. Frequency tables and histograms 8 min ◈ 5
  2. Mean, median, mode, and skew 9 min ◈ 6
  3. Variance and standard deviation 11 min ◈ 6
  4. Quartiles, IQR, and the box plot 10 min ◈ 6
  5. z-scores, the empirical rule, and Chebyshev 9 min ◈ 7
  6. Grouped data and the geometric mean 9 min ◈ 5
  7. R descriptives and summary() 8 min ◈ 7

Describing a Relationship: Correlation and the Least-Squares Line

34 cards
  1. Scatter plots and covariance 9 min ◈ 4
  2. Pearson r and what it means 10 min ◈ 5
  3. The least-squares line 11 min ◈ 5
  4. Interpreting and predicting with the line 9 min ◈ 4
  5. R² and the sums of squares 10 min ◈ 6
  6. Outliers, influential points, and refitting 10 min ◈ 4
  7. Reading summary(lm) as description 9 min ◈ 6

Probability

32 cards
  1. Sample spaces, events, and the complement 8 min ◈ 5
  2. The addition rule 8 min ◈ 4
  3. Conditional probability and the multiplication rule 10 min ◈ 7
  4. Independence versus mutually exclusive 9 min ◈ 5
  5. Contingency tables and tree diagrams 10 min ◈ 5
  6. Reversing the condition, and counting 9 min ◈ 6

Discrete Random Variables

42 cards
  1. Random variables and their distributions 8 min ◈ 5
  2. Expected value and variance of a discrete random variable 10 min ◈ 6
  3. Linear transformations and sums of random variables 9 min ◈ 6
  4. The binomial distribution 10 min ◈ 7
  5. Binomial cumulative probabilities and pbinom 9 min ◈ 5
  6. The Poisson distribution 9 min ◈ 7
  7. Binomial or Poisson? 9 min ◈ 6

Continuous Random Variables and the Normal Distribution

35 cards
  1. Density curves and area as probability 7 min ◈ 5
  2. The normal family and standardising 8 min ◈ 6
  3. Normal probabilities with the cumulative table 10 min ◈ 6
  4. Inverse problems: percentiles and critical values 10 min ◈ 7
  5. The normal approximation to the binomial 9 min ◈ 4
  6. pnorm, qnorm and the midterm checkpoint 9 min ◈ 7

Sampling Distributions and the Central Limit Theorem

35 cards
  1. A statistic is a random variable 9 min ◈ 5
  2. Mean and variance of X̄ 10 min ◈ 7
  3. Normal population, so X̄ is normal for any n 9 min ◈ 4
  4. The Central Limit Theorem 10 min ◈ 6
  5. Individual, mean, or total? 10 min ◈ 6
  6. The sampling distribution of p̂ 9 min ◈ 7

Confidence Intervals for a Mean, and Minimum Sample Size

39 cards
  1. Estimate ± critical × SE: the z-interval 10 min ◈ 6
  2. What "95 % confident" means 9 min ◈ 5
  3. Student’s t and its table 9 min ◈ 6
  4. The t-interval 10 min ◈ 5
  5. Large df and the ∞ row 8 min ◈ 5
  6. Minimum sample size for a mean 9 min ◈ 7
  7. Choosing z or t, and the CI checkpoint 9 min ◈ 5

Hypothesis Testing: the Framework and One-Sample Tests

43 cards
  1. Null and alternative hypotheses 9 min ◈ 5
  2. Type I and Type II errors 9 min ◈ 5
  3. The four steps and the critical-value route 11 min ◈ 5
  4. p-values 10 min ◈ 7
  5. The one-sample t-test and bracketing p 11 min ◈ 6
  6. Conclusions in business context 8 min ◈ 4
  7. The CI and the two-sided test agree 8 min ◈ 4
  8. Reading t.test output 9 min ◈ 7

Comparing Two Means: Independent and Paired

42 cards
  1. Independent or paired 8 min ◈ 6
  2. The sampling distribution of a difference 8 min ◈ 6
  3. Welch t with the minimum-df rule 12 min ◈ 8
  4. Welch confidence interval for the difference 8 min ◈ 4
  5. Pooled t when the variances are equal 10 min ◈ 6
  6. Paired differences 11 min ◈ 5
  7. Choosing the case and reading t.test(x, y) 9 min ◈ 7

Inference for Proportions

29 cards
  1. p̂ and its confidence interval 9 min ◈ 6
  2. Minimum n for a proportion 8 min ◈ 5
  3. The one-proportion z-test 10 min ◈ 5
  4. Two proportions: pooled test, unpooled interval 11 min ◈ 7
  5. Means or proportions, and prop.test 8 min ◈ 6

Inference for Regression

38 cards
  1. The model assumptions and the residual standard error 9 min ◈ 7
  2. Standard error of the slope and the t-test 11 min ◈ 7
  3. Confidence interval for the slope, and testing r 9 min ◈ 5
  4. Residual plots and what they catch 8 min ◈ 7
  5. Predicting at x* and the limits of the line 10 min ◈ 5
  6. Reading summary(lm) for inference 9 min ◈ 7

Choosing the Procedure, Reading R, and Exam Craft

35 cards
  1. Which parameter, which estimator 9 min ◈ 5
  2. Which table, which df 8 min ◈ 7
  3. The cheat-sheet formula inventory 10 min ◈ 8
  4. Hand versus R: the three mismatches 8 min ◈ 6
  5. The mock final 12 min ◈ 9
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