STA 2023 Exam Review: Descriptive Stats, Probability, Sampling and Inference

Terms in this set (30)

1. Population vs sample; parameter vs statisticA population is the entire group of interest; a sample is a subset. A parameter describes a population (mu, sigma, p); a statistic describes a sample (x-bar, s, p-hat).
2. Categorical vs quantitative variablesCategorical variables place individuals into groups (eye color). Quantitative variables take numerical values where arithmetic makes sense (height).
3. Mean vs median in a right-skewed distributionThe mean is pulled toward the long right tail, so mean > median. The median is resistant to outliers.
4. How is the 1.5 x IQR rule used to flag outliers?IQR = Q3 - Q1. Values below Q1 - 1.5*IQR or above Q3 + 1.5*IQR are potential outliers.
5. What does the standard deviation measure?The typical distance of observations from the mean. It is the square root of the variance and is never negative.
6. State the empirical (68-95-99.7) rule.For a roughly 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. Compute the z-score for x = 85 when mu = 70 and sigma = 10.z = (x - mu) / sigma = (85 - 70) / 10 = 1.5, so 85 is 1.5 SD above the mean.
8. Properties of the correlation coefficient rr ranges from -1 to 1, measures the strength and direction of a linear relationship, has no units, and is sensitive to outliers. Correlation does not imply causation.
9. Interpret the slope in y-hat = 20 + 3x.For each one-unit increase in x, the predicted y increases by 3 units on average.
10. What is a residual?Residual = observed y - predicted y-hat. The least-squares line minimizes the sum of squared residuals.
11. What does r^2 tell you?The proportion of variation in y explained by the linear relationship with x.
12. Observational study vs experimentIn an observational study researchers measure without intervening. In an experiment they impose treatments, and with random assignment it can show cause and effect.
13. Name four probability sampling methods.Simple random sample, stratified sample (random within groups), cluster sample (randomly choose whole groups) and systematic sample (every kth individual).
14. What is the complement rule and the addition rule?P(not A) = 1 - P(A). P(A or B) = P(A) + P(B) - P(A and B).
15. When are events A and B independent?When P(A and B) = P(A) * P(B), equivalently P(A | B) = P(A). Knowing one occurred does not change the probability of the other.
16. Mutually exclusive vs independentMutually exclusive events cannot both occur (P(A and B) = 0). Two events with positive probability that are mutually exclusive are never independent.
17. Conditional probability formulaP(A | B) = P(A and B) / P(B).
18. Conditions for a binomial setting and its mean and SDFixed n trials, two outcomes, independent trials, constant p. Mean = n*p; SD = sqrt(n*p*(1 - p)).
19. State the Central Limit Theorem.For large n (often n >= 30), the sampling distribution of x-bar is approximately normal with mean mu and standard error sigma/sqrt(n), regardless of the population shape.
20. What happens to the standard error when sample size quadruples?It is cut in half, since SE = sigma / sqrt(n).
21. Correct interpretation of a 95 percent confidence intervalWe are 95 percent confident the interval captures the true parameter; in repeated sampling, about 95 percent of such intervals would contain it.
22. How do confidence level and sample size affect margin of error?Higher confidence gives a wider margin of error. Larger sample size gives a smaller margin of error.
23. Formula for a confidence interval for a population proportionp-hat +/- z* x sqrt(p-hat(1 - p-hat)/n). For 95 percent confidence, z* = 1.96.
24. When do you use a t distribution instead of z for a mean?When the population standard deviation is unknown and estimated with s; degrees of freedom = n - 1.
25. Null vs alternative hypothesisH0 is the claim of no effect or no difference (e.g., mu = 50). Ha is what you seek evidence for (mu > 50, mu < 50, or mu not equal to 50).
26. What is a p-value?The probability, assuming H0 is true, of getting a result at least as extreme as the one observed. Small p-values are evidence against H0.
27. Decision rule with significance level alpha = 0.05If p-value <= 0.05, reject H0. If p-value > 0.05, fail to reject H0 (never say 'accept H0').
28. Type I vs Type II errorType I: rejecting a true H0 (probability alpha). Type II: failing to reject a false H0 (probability beta). Power = 1 - beta.
29. Test statistic for a one-sample z test for a proportionz = (p-hat - p0) / sqrt(p0(1 - p0)/n), where p0 is the value in the null hypothesis.
30. Common pitfall: does a p-value of 0.03 mean a 3 percent chance H0 is true?No. It means a 3 percent chance of data this extreme if H0 were true; it is not the probability that H0 is true.