STT 200 Exam Review: Data Analysis, Probability, Confidence Intervals, Hypothesis Tests and Regression

Terms in this set (30)

1. Population vs sample; parameter vs statisticA population is the entire group of interest and a parameter describes it (mu, p). A sample is a subset actually measured and a statistic describes it (x-bar, p-hat).
2. Categorical vs quantitative variablesCategorical variables place individuals into groups (major, eye color); quantitative variables take numerical values for which arithmetic makes sense (height, income).
3. Mean vs median when a distribution is right-skewedThe mean is pulled toward the long right tail, so mean > median. The median is resistant to outliers and better describes the center of skewed data.
4. IQR and the 1.5 x IQR outlier ruleIQR = Q3 - Q1. A value is flagged as an outlier if it is below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR.
5. Z-score formula and meaningz = (x - mean) / standard deviation. It tells how many standard deviations a value is above (positive) or below (negative) the mean.
6. 68-95-99.7 ruleFor a normal distribution, about 68 percent of values fall within 1 SD of the mean, 95 percent within 2 SD, and 99.7 percent within 3 SD.
7. Observational study vs experimentIn an observational study researchers measure without intervening; in an experiment they assign treatments. Only well-designed randomized experiments can establish cause and effect.
8. Simple random sample and a common source of biasAn SRS gives every possible sample of size n an equal chance of selection. Voluntary response samples are biased because people with strong opinions are more likely to respond.
9. Addition rule for probabilityP(A or B) = P(A) + P(B) - P(A and B). If A and B are disjoint, P(A and B) = 0.
10. Independent vs disjoint events: common pitfallDisjoint events cannot happen together. Independent events do not affect each other's probabilities: P(A and B) = P(A) x P(B). Disjoint events with nonzero probabilities are never independent.
11. Conditional probability formulaP(A | B) = P(A and B) / P(B): the probability of A given that B has occurred.
12. Expected value of a discrete random variableE(X) = sum of x x P(x), the long-run average value of X over many repetitions.
13. Conditions for a binomial settingA fixed number n of trials, two outcomes (success or failure), independent trials, and the same probability of success p on each trial.
14. Binomial mean and standard deviationMean = n x p; standard deviation = square root of n x p x (1 - p).
15. Sampling distribution of the sample meanx-bar has mean mu and standard deviation sigma divided by square root of n. Larger samples give less variable sample means.
16. Central Limit TheoremFor a large enough sample size (a common guideline is n of at least 30), the sampling distribution of x-bar is approximately normal, regardless of the population's shape.
17. General form of a confidence intervalEstimate plus or minus margin of error, where margin of error = critical value x standard error.
18. Correct interpretation of a 95 percent confidence intervalWe are 95 percent confident the interval captures the true parameter; 95 percent of intervals built this way would contain it. It is not a 95 percent chance that the parameter is in this specific interval.
19. How does sample size affect the margin of error?Margin of error shrinks as n grows, in proportion to 1 / square root of n; to cut it in half you need about four times the sample size.
20. Confidence interval for a proportionp-hat plus or minus z* x square root of [p-hat(1 - p-hat) / n]. For 95 percent confidence, z* = 1.96.
21. Null vs alternative hypothesisThe null hypothesis H0 states no effect or no difference (parameter equals a specific value). The alternative Ha states what we are looking for evidence of (greater than, less than or not equal).
22. Definition of a p-valueThe probability, assuming H0 is true, of getting a test statistic at least as extreme as the one observed. A small p-value is evidence against H0.
23. Decision rule using significance level alphaIf p-value is at most alpha (often 0.05), reject H0; otherwise fail to reject H0. We never accept or prove H0.
24. Type I vs Type II errorType I: rejecting H0 when it is actually true (probability alpha). Type II: failing to reject H0 when it is actually false (probability beta). Power = 1 - beta.
25. When should you use a t procedure instead of z for a mean?When the population standard deviation sigma is unknown and estimated by the sample s; use a t distribution with n - 1 degrees of freedom.
26. Correlation coefficient r: key propertiesr ranges from -1 to 1, measures the strength and direction of a linear relationship, has no units, and is not resistant to outliers.
27. Least-squares regression line and slope interpretationy-hat = b0 + b1 x. The slope b1 is the predicted change in y for each one-unit increase in x.
28. What is a residual?Residual = observed y - predicted y-hat. The least-squares line minimizes the sum of squared residuals.
29. Meaning of r^2 in simple linear regressionThe fraction of the variation in y explained by the linear relationship with x. For r = 0.6, r^2 = 0.36, so 36 percent is explained.
30. Extrapolation pitfallUsing a regression line to predict far outside the range of observed x values is unreliable because the linear pattern may not continue.