STT 231 EXAM 2 STUDY GUIDE 2026/2027 ACCURATE QUESTIONS WITH CORRECT DETAILED SOLUTIONS || 100% GUARANTEED PASS NEWEST VERSION

STT 231 EXAM 2 STUDY GUIDE 2026/2027 ACCURATE QUESTIONS WITH CORRECT DETAILED SOLUTIONS || 100% GUARANTEED PASS NEWEST VERSION 1. what two conditions must be met in order for the CLT to apply for proportional testing? - ANSWER 1: sample must be independent and identically distributed; like random assignment/sampling 2: sample must be sufficiently large 2. normal density curve - ANSWER symmetric about the mean μ; has standard deviation σ; total area under the curve = 1.0; values of the random variable X on x-axis; probabilities are represented by areas under the curve; 3. what do the numbers in the N(0,1) equation represent? - ANSWER the first number is the mean (mu), and the second is the SD (sigma) 4. what is the equation for a standard normal curve/distribution, and what do the axes represent? - ANSWER N(0,1) the x axis represents z-scores, and the y is the probability 5. what is the domain for a standard normal curve? which particular interval are we interested in? - ANSWER the actual domain=infinite, but we are interested mostly in (mu +/- 3sigma) 6. difference between pnorm and qnorm commands - ANSWER pnorm: gives proportion/percent of data within the given range qnorm: gives the cutoff range for the percentile of data inputted 7. what are the required arguments for pnorm? qnorm? - ANSWER pnorm(upper cutoff, mean, SD) qnorm(upper percentile cutoff, mean, SD) 8. when do you use the =false argument? - ANSWER during p/qnorm commands, when you are interested in the right side distribution 9. normal model for sampling distribution of pi hat - ANSWER still follows the rule of standard normal curve (N(0,1)), but it uses N(pi, SE equation) because 10. what is standard error? how do you interpret the results? - ANSWER it measures how close the current sample data reflects the overall population predicted data, a high standard error value represents that your sample is not very reflective of the population and is very spread out, vice versa for low 11. how do SE and sample size n relate? - ANSWER as n increases, SE decreases, inverse relationship. 12. Population Mean - ANSWER μ (mu) - quantitative summary 13. Sample Mean - ANSWER x ̅ - quantitative summary 14. Population Standard Deviation - ANSWER σ (sigma) - quantitative summary 15. Sample Standard Deviation - ANSWER s - quantitative summary 16. Population Proportion - ANSWER pi - categorical summary - true proportion 17. Sample Proportion - ANSWER pi hat - categorical summary 18. Statistical Model - ANSWER set of assumptions (often mathematical) concerning the process that generates data at random and the relationship between one or more random variables. Models are usually an approximation of reality. 19. Randomness - ANSWER broadly defined as any process that generates data in a manner that is unpredictable in the short term, but predictable in the long-run. 20. Parameter - ANSWER a number that describes some aspect of a statistical model(population). These values are typically unknown and are the subject of scientific inquiry. 21. Statistic - ANSWER a number that describes some aspect of an observed sample 22. Fixed - ANSWER all outcomes 23. Random - ANSWER choosing one random outcome (sampling) 24. Sampling Variability - ANSWER the natural tendency of randomly drawn samples to differ, one from another 25. Inference Diagram - ANSWER see pg. 59 of notes 26. Sampling Distribution - ANSWER a distribution that describes the behavior of a statistic. Specifically, it describes the values a statistic can take on, and how likely they are to do so, across all possible samples of the same size from a given generative model. 27. Standard Error - ANSWER standard deviation of a statistic. measured the approx. distance between a statistic and the parameter (center) it estimates. can be represented using different notations as well: - σ [subscript] statistic - SE (statistic) - SE [subscript] statistic 28. Sample Size (n) - ANSWER influences the behavior of the sample statistic. as the sample size increases, the standard error of a statistic decreases with the rate of 1/sqrt (n). 29. *same as statistics produced from larger samples tend to be more precise estimates of model parameters 30. Normal Distribution - ANSWER Symmetric and unimodal (bell shaped). points are all on the line on the qq plot as well 31. Central Limit Theorem - ANSWER Describing how a sampling distribution of a statistic will behave. So long as two conditions are met: 1. Data are sampled from independent and identical distributions (IID). Independence is often guaranteed in an observational study by taking a random sample from a population. It can also be guaranteed in the context of a controlled experiment if we randomly assign individuals to treatment groups. 2. Sample must be sufficiently large. We must gather a sufficiently large sample of data, regardless of whether it is an observational study or controlled experiment, for the Central Limit Theorem to take effect. *trying to get to a bell-curve 32. Equation of normal curve (CLT) - ANSWER [1/sqrt (2pi * σ^2)] [e^-(x mu)^2/2σ^2] pi = 3.14 e = 2.718 x = value mu = population mean σ = population sd. 33. Changing the mean of the normal curve - ANSWER changes the location of the curve (higher mu, shifting right) 34. Changing the standard deviation of the curve - ANSWER compresses of stretches the curve without its location changing 35. If the normal curve has mu and σ - ANSWER the equation of the curve is abbreviated as: N (mu, 0) 36. Higher the sample size, - ANSWER more accurate the results 37. Consider taking samples of size