Course Standards

You correctly classify variables including tricky cases like Likert scales and postal codes. You assign the right notation symbol in a scenario you haven't seen before — and you can explain why a parameter is usually unknown while a statistic is computed from data.

Given a described study, you correctly name the sampling method and explain at least one specific way the design could systematically over- or under-represent part of the population — including whether that bias pushes the estimate up or down.

You choose the right graph type for a given variable (including knowing why a bar chart, not a histogram, belongs with categorical data). You read absolute, relative, and cumulative frequencies without confusion. Given a misleading graph, you identify the specific technique used and what it makes the reader think incorrectly.

You correctly compute all three measures from unsorted raw data (sorting first for the median) and from a frequency table using weighted calculations — without a calculator.

You use n−1, not n, in the sample variance formula and can explain why. You correctly compute IQR and apply both fences (Q1 − 1.5×IQR and Q3 + 1.5×IQR) to classify each value as an outlier or not.

Given a described or displayed distribution (skewed, symmetric, with outliers), you choose and justify both the right measure of center and the right measure of spread. You correctly predict which way an outlier will pull the mean without pulling the median. You never pair mean with IQR or median with SD.

You correctly compute z-scores and locate percentiles. Before using the 68–95–99.7 rule, you check whether the distribution is approximately normal — and you explain why the rule doesn't apply if it isn't. You correctly identify skewness direction from a histogram or description (the tail points in the direction of the skew, not the peak).

You identify whether events are mutually exclusive before choosing which addition rule to apply. You correctly compute union, intersection, and complement probabilities. Your Venn diagrams accurately represent the given scenario.

Given a pair of events, you correctly classify them as mutually exclusive, independent, both (impossible for events with positive probability), or neither — with a written explanation of why. You don't confuse "can't happen together" with "don't affect each other."

You correctly restrict the sample space when conditioning — dividing by P(B), not P(S). You build accurate tree diagrams and read off the right joint and conditional probabilities. You apply P(A∩B) = P(B)·P(A|B) for dependent events.

Given a scenario, you identify which conditional probability is actually being asked for and don't reverse the direction. In a medical test or legal scenario, you correctly distinguish P(positive | disease) from P(disease | positive). You apply both independence tests — P(A|B) = P(A) and P(A∩B) = P(A)·P(B) — and explain what each checks.

For a problem you haven't seen before, you correctly decide whether order matters before picking a formula. You apply the right formula and use the result to calculate a probability. You don't use a permutation formula when the problem is asking about selections where order is irrelevant.

You build a correct PMF from a described scenario and verify ΣP(X=x) = 1. You compute E(X²) and [E(X)]² separately — not as the same thing — and use them correctly in the variance formula.

In a real-world context (insurance, games, medical decisions), you correctly explain what E(X) represents without saying it's the "most likely" outcome. You give an example where the expected value is not a possible value of X. You explain in plain language why E(X²) and [E(X)]² are different quantities.

You explicitly check and justify all four BINS conditions before computing anything. You correctly translate at least two different cumulative language forms into probability expressions without confusing "exactly k" with "at least k." You compute μ and σ using the binomial formulas.

You always standardize X before using the table. You correctly compute all three region types — including using the complement for right-tail areas and subtracting two table values for middle regions. You don't add left-tail areas when finding P(a < Z < b).

Given a probability (which may be a right-tail area requiring a complement step first), you correctly locate z* in the table and then convert back to the original scale using x = μ + z*σ. You don't stop at z* without unstandardizing.

You use σ/√n (the standard error) — not σ alone — whenever you compute a probability for a sample mean. You can state the mean and SE of the sampling distribution for any given μ, σ, and n.

You correctly explain that the CLT is a statement about x̄ (the distribution of sample means across many samples) — not about individual data values becoming more normal. You correctly describe how increasing n changes the spread of the sampling distribution. You state the condition under which the CLT applies.

You build a correct interval for at least two different confidence levels, selecting the right z* each time. You correctly solve for n given a target margin of error, σ, and confidence level.

You state the correct interpretation without attaching a probability to μ being in any specific interval. You explain specifically why the standard misinterpretation is wrong — μ is fixed, not random. You explain what "95% confident" means in terms of what would happen if you repeated the procedure many times.

You use df = n−1 (not n) to look up t*. You explicitly state why t is required in the given scenario. You verify that the population is approximately normal (especially important for small n).

You use p̂ (not p₀ from a null hypothesis) in the standard error formula. You explicitly check np̂ ≥ 5 and n(1−p̂) ≥ 5 before building the interval. You correctly solve for n using p* = 0.5.

You state both hypotheses before touching any numbers. Your Hₐ correctly reflects the research question's direction (one-tailed or two-tailed), chosen in advance. Your conclusion refers back to the original research context — not just "reject H₀."

You define p-value as the probability of observing data this extreme or more extreme, assuming H₀ is true — not as the probability that H₀ is true. You use "fail to reject" language correctly and explain what it does not mean. Given a scenario, you correctly identify which type of error (false positive or false negative) was made.

You use p₀ in the proportion test standard error — not p̂ — and you can explain why (you're measuring how extreme the result is under the assumption that H₀ is true). You use df = n−1 in the t-test. Given a scenario description, you identify the correct test and state the justification.

You correctly compute r and r². You describe scatter plots using all four characteristics. You correctly interpret r = 0 as no linear relationship — not as no relationship of any kind.

You report r² (not r) as the proportion of variance explained. You identify a concrete confounding variable mechanism — not just the phrase "correlation doesn't equal causation" — that would explain an observed association without causation.

You correctly compute b and a. Your slope interpretation includes "predicted" and "on average." You flag when the intercept interpretation is not meaningful (x = 0 outside the observed data range). You correctly calculate and interpret a residual as actual minus predicted.

You identify whether a prediction is interpolation or extrapolation and explain what risk extrapolation introduces. You correctly set up and execute the significance test for r. On a residual plot, you identify a curved pattern as evidence of non-linearity and a fan shape as evidence of heteroscedasticity.

Given a large-sample scenario where r = 0.15 and p < 0.001, you correctly identify this as statistically significant but practically weak, using r² = 0.0225 as the relevant measure. You explain that statistical significance tells you the relationship is real, not that it's useful.

You correctly compute all expected frequencies and the χ² statistic. You check the E ≥ 5 condition explicitly. Your conclusion uses association language — not causation — and is stated in the context of the original research question.

You correctly identify variable types and select the right method with a written justification. You report effect size alongside the p-value — not p-value alone — in your conclusion.