STT 231 - EXAM 2 QUESTIONS WITH VERIFIED ANSWERS LATEST UPDATE 2026

STT 231 - EXAM 2 QUESTIONS WITH VERIFIED ANSWERS LATEST UPDATE 2026 what two conditions must be met in order for the CLT to apply for proportional testing? - Answers 1: sample must be independent and identically distributed; like random assignment/sampling 2: sample must be sufficiently large normal density curve - Answers 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; what do the numbers in the N(0,1) equation represent? - Answers the first number is the mean (mu), and the second is the SD (sigma) what is the equation for a standard normal curve/distribution, and what do the axes represent? - Answers N(0,1) the x axis represents z-scores, and the y is the probability what is the domain for a standard normal curve? which particular interval are we interested in? - Answers the actual domain=infinite, but we are interested mostly in (mu +/- 3sigma) difference between pnorm and qnorm commands - Answers pnorm: gives proportion/percent of data within the given range qnorm: gives the cutoff range for the percentile of data inputted what are the required arguments for pnorm? qnorm? - Answers pnorm(upper cutoff, mean, SD) qnorm(upper percentile cutoff, mean, SD) when do you use the =false argument? - Answers during p/qnorm commands, when you are interested in the right side distribution normal model for sampling distribution of pi hat - Answers still follows the rule of standard normal curve (N(0,1)), but it uses N(pi, SE equation) because what is standard error? how do you interpret the results? - Answers 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 how do SE and sample size n relate? - Answers as n increases, SE decreases, inverse relationship. normal model for a sampling distribution of x bar - Answers still N(0,1) template, but the mean is represented by mu, and the SD is sigma/square root of n when should you use normal model sampling distribution of x bar and when for pi hat? - Answers x bar if you are given mu in the problem, pi hat if you are given pi in the problem if you are given a problem that gives the sample mean and asks for the proportion greater than or equal to a z score, what would you do? - Answers set up the equation with the pnorm command using the standard normal model, with pnorm(the value,0,1) how do you create a qqplot in R? - Answers two commands required: 1: qqnorm(data set$variable) 2: qqline(data set$variable) what would a straight qq plot indicate? - Answers the sample data can be represented by a normal distribution model (unimodal, no skew, centered at the mean) what would a concave up qq plot indicate? - Answers right-skewed data what would a concave down qq plot indicate? - Answers the data is skewed/tailed to the left what does an s shaped qq plot represent? - Answers a plot that looks normally distributed but the tails are either too fat/too thin (granularity differences) with few outliers how to predict whether your sample size is large enough to assume a normal distribution? - Answers apply the success-failure condition what is the null distribution? - Answers the sampling distribution based off of the null value? p-value - Answers assuming the null hypothesis is true, the probability that you will observe data as favorable or more favorable for the alternative hypothesis as the current observed data what do high and low p values mean in a general sense? - Answers a high p-value :0.10 means that 10% of the time, you could expect to see your sample statistic occur under the null model, lower values 0.05 means that only 5% of the time would the null distribution support your sample statistic what are the various cutoff values for a p value? - Answers less than 0.001 (extremely strong evidence against null) 0.001 to 0.01 (very strong evidence) 0.01 to 0.05 (strong evidence) 0.05 to 0.10 (some evidence) more than 0.10 (little evidence against null hypothesis) what is a z-score - Answers number of standard deviations away from the mean one-proportion z test? - Answers describes the position of data in terms of the mean (0) and is measured in standard deviations. Basically the number of standard deviations/standard errors a certain data point is from the mean of the null distribution difference between p values and z scores - Answers z score compares a current data point to the data point's mean of the null model (0), and a p value would quantify the probability of getting that data point under the null model how to interpret large/small z-score values - Answers large z score: sample data is either larger/smaller than the null model small z score: null model can be a correct representation because their is little different in terms of standard error between your observed sample and the null model when is Cohen's H used? - Answers when you want to gauge how wrong/right the null model is for a single-proportion test what is the relationship between p value and effect size? - Answers as the effect size becomes more extreme either positively or negatively, the p value decreases, because the null model becomes more wrong which statistics consider n, and which do not? - Answers sample size considered for p value and test statistiscs, but not for effect size what are the 4 magnitudes for Cohen's H values? - Answers less than 0.2: null model wrong but can still be used as a "correct model" 0.2 to 0.5: null model wrong but only proved through statistical testing 0.5 to 0.8: trained observer would notice null is incorrect greater than 0.8: null model is so wrong it is noticeable with the naked eye what conditions need to be met in order for the CLT to apply for mean sampling? - Answers 1: the model must be normally distributed 2: the sample size must be sufficiently large 3: the cases must be independent and identically distributed why do we use s instead of sigma for t-distributions? - Answers because if we are estimating mu, there is an even slimmer likelihood we would know the value of sigma, and sigma introduces additional variability N(0,1) cannot handle what is degrees of freedom? - Answers maximum number of free samples of the data, found by subtracting 1 from n when do you use p norm and when do you use pt - Answers pt for t distributions when you are given the mean mu, pnorm for proportional tests with a normal distribution