STAT 503 FINAL EXAM 2023 SOLVED 100% CORRECT

Is a quantitative variable always measured in numbers? - ANSWER-Yes Is any measurement that you record from a sample a variable? - ANSWER-False What is a statistic? - ANSWER-The measure that is taken from the whole sample as a summary of the sample Sample data skewed to the left, then longer tail is at the... - ANSWER-Left What is sensitive to outliers? - ANSWER-Median Formula to calculate standard deviation - ANSWER-s = sqrt(sum(x1-xbar)^2 / n-1) How to calculate degrees of freedom? - ANSWER-n-1 What is the first quartile? - ANSWER-Median of lower half What is the third quartile - ANSWER-Median of upper half What is included in a box plot summary? - ANSWER-Q0 = minimum Q1 = median of lower half Q2 = median Q3 = median of upper half Q5 = maximum What is the the interquartile range (IQR)? - ANSWER-Q3 - Q1 (shown inside box plot) What is an outlier? - ANSWER-Any data that is Q3 + 1.5IQR or Q1 - 1.5 IQR When is a phenomenon random? - ANSWER-When it has uncertain outcomes in a short run (sample) but show regular distribution in a long run (population) What is an outcome? - ANSWER-Observation of a variable What is a probability model? - ANSWER-A mathematical description of a random phenomenon consisting of 2 parts (sample space and way of assigning probability to event) What is the multiplication rule? (independent) - ANSWER-P(AB) = P(A) P(B|A) = P(B) P(A|B) What is the addition rule? (disjoint) - ANSWER-P(A or B) = P(A) + P(B) - P(AB) If A and B are disjoint, the must be dependent. - ANSWER-TRUE Why is a probability tree diagram used? - ANSWER-To show multiple variables according to stages (the order that they happen) What is written on each segment in a probability tree? - ANSWER-A conditional probability What probability is at the end of the branch on a probability tree? - ANSWER-The product of the probabilities of the segments of that branch What are all ultimate outcomes of probability tree? - ANSWER-Disjoint outcomes, non-overlapping "Sensitivity" (HIV example) - ANSWER-P(T+| HIV+) "Specificity" (HIV example) - ANSWER-P(T- | HIV-) Positive result (HIV example) - ANSWER-P(T+) = true positive + false positive Positive predictive value (PPV) - ANSWER-P(True positive | T+) How can PPV be improved? - ANSWER-If disease prevalence rate is higher Population mean E(X) - ANSWER-µ(x) = sum[xi * P(X = xi)] Population variance Var(X) - ANSWER-σ^2(x) = sum[(xi-µ)^2 * P(X = xi)] Population standard deviation - ANSWER-σ(x) = sqrt(σ^2(x)) Compute Var(X+Y) - ANSWER-σ^2(1) + σ^2(2) or (2σ^2) Compute Var(X-Y) - ANSWER-σ^2(1) + σ^2(2) or (2σ^2) Compute Var(X+Y/2) - ANSWER-(σ^2(1) + σ^2(2))/4