STAT 1450 Final Review: Sampling, Probability, Confidence Intervals and Regression

Terms in this set (30)

1. Categorical vs quantitative variableCategorical variables place individuals into groups (eye color); quantitative variables take numerical values where arithmetic makes sense (height).
2. Mean vs median: which is resistant to outliers?The median is resistant; the mean is pulled toward outliers and the long tail of a skewed distribution.
3. In a right-skewed distribution, how do the mean and median compare?The mean is typically greater than the median because the long right tail pulls the mean upward.
4. How is the IQR calculated and how is it used to flag outliers?IQR = Q3 - Q1. A value is a suspected outlier if it is below Q1 - 1.5*IQR or above Q3 + 1.5*IQR.
5. State the 68-95-99.7 rule.For a Normal distribution, about 68% of values lie within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3.
6. Formula for a z-score and what it meansz = (x - mu)/sigma. It tells how many standard deviations a value lies above (positive) or below (negative) the mean.
7. Exam scores are Normal with mean 70 and SD 10. What is the z-score of 85?z = (85 - 70)/10 = 1.5, so the score is 1.5 standard deviations above the mean.
8. Observational study vs experimentIn an observational study researchers measure without intervening; in an experiment they impose treatments. Only well-designed experiments can show causation.
9. What is a confounding variable?A variable related to both the explanatory variable and the response, so its effect cannot be separated from the effect of the explanatory variable.
10. Three principles of experimental designControl (comparison group, reduce other variation), randomization (random assignment to treatments), and replication (enough subjects to see real effects).
11. What is a simple random sample (SRS)?A sample of size n chosen so every possible set of n individuals has an equal chance of being selected.
12. Name two common sources of bias in sampling.Voluntary response bias (people choose to respond, often with strong opinions) and undercoverage (some groups left out of the sampling frame). Nonresponse bias is another.
13. Addition rule for P(A or B)P(A or B) = P(A) + P(B) - P(A and B). If A and B are disjoint, P(A and B) = 0.
14. When are two events independent, and what is the multiplication rule?A and B are independent if knowing one occurs doesn't change the probability of the other. Then P(A and B) = P(A)*P(B).
15. Conditional probability formulaP(A | B) = P(A and B) / P(B): the probability of A given that B has occurred.
16. Conditions for a binomial settingFixed number n of trials, each trial is success or failure, trials are independent, and the probability of success p is the same each trial.
17. Mean and SD of a binomial random variablemean = n*p and SD = sqrt(n*p*(1-p)).
18. What does the Central Limit Theorem say?For a large enough sample size, the sampling distribution of the sample mean is approximately Normal with mean mu and SD sigma/sqrt(n), whatever the population shape.
19. Parameter vs statisticA parameter describes a population (mu, p) and is usually unknown; a statistic is computed from a sample (x-bar, p-hat) and used to estimate the parameter.
20. Correct interpretation of a 95% confidence intervalWe are 95% confident the interval captures the true parameter; the method produces intervals that capture it in about 95% of repeated samples.
21. How does increasing sample size affect a confidence interval's margin of error?Margin of error decreases (roughly by 1/sqrt(n)); quadrupling n halves it. Raising the confidence level widens the interval.
22. Formula for a confidence interval for a population proportionp-hat +/- z* * sqrt(p-hat*(1-p-hat)/n), where z* is 1.96 for 95% confidence.
23. What is a p-value?The probability, assuming the null hypothesis is true, of getting a result at least as extreme as the one observed. Small p-values are evidence against H0.
24. If p-value = 0.03 and alpha = 0.05, what do you conclude?Since 0.03 < 0.05, reject H0: the result is statistically significant at the 5% level. It does not prove H0 false or show a large effect.
25. Type I vs Type II errorType I: rejecting a true H0 (false positive); its probability is alpha. Type II: failing to reject a false H0 (false negative).
26. When should you use a t procedure instead of z for a mean?When the population standard deviation is unknown and estimated by the sample SD s. The t distribution has heavier tails and degrees of freedom n - 1.
27. Interpret a regression slope b = 2.5 for predicting weight (lb) from height (in).For each additional inch of height, predicted weight increases by 2.5 lb on average.
28. What does r^2 represent in linear regression?The fraction of the variation in the response variable explained by the linear relationship with the explanatory variable.
29. What is a residual?Residual = observed y - predicted y-hat. A residual plot with no pattern suggests a linear model is appropriate.
30. Why is extrapolation risky?Using a regression line to predict far outside the range of observed x values assumes the pattern continues, which often isn't true.