STAT 503 Final EXAM 2022/2023 Questions and Answers

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 ...

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 How to denote a binomial variable - ANSWER X~Bin(n, p) (n is the sample size, p is the constant proportion of success) What is X defined as in a binomial - ANSWER The number of successes Mean of binomial variable - ANSWER np Standard deviation of binomial variable - ANSWER sqrt(np(1-p)) Effect of changing p - ANSWER Small p (0.05) is skewed right Mid p (0.5) is symmetric Large (0.95) is skewed left Effect of increasing n - ANSWER Distribution becomes more bell-shaped Normal approximation to the binomial - ANSWER When n gets large, binomial distribution gets to bell shape around the mean, except when p gets to an extreme value Bell shape rule - 68% of values are... - ANSWER Within 1 standard deviation from the mean Bell shape rule - 95% of values are... - ANSWER Within 2 standard deviations from the mean Bell shape rule - 99.7% of values are... - ANSWER Within 3 standard deviations from the mean Standardize using z-score - ANSWER X - µ/σ When does X approximately follow the normal approximation to binomial? - ANSWER When np and np(1-p) are both > 10 What is the Xbar - ANSWER Sampling distribution of sample mean Central Limit Theorem requirements - ANSWER Sample size greater than 25 OR Population distribution is normal CLT set-up - ANSWER Xbar~Normal(µ, σ/sqrt(n)) How to calculate margin of error (ME) - ANSWER Za/2, σ/sqrt(n) What is the margin of error - ANSWER The width of the confidence interval that you can build on possible sample means so that 1-a (success rate) of them would contain µ The smaller CI, the... ...ME - ANSWER Smaller ME The larger n is, the ... ...ME - ANSWER Smaller ME Z-method assumptions - ANSWER N is > 25 or X~N(µ, σ) σ is known Z-method equation - ANSWER Xbar +/- z(σ/sqrt(N)) T-method assumptions - ANSWER N is > 25 or X~N(µ, σ) σ is unknown T-method equation - ANSWER Xbar +/- t(df)(s/sqrt(n)) Does a bigger or smaller SE make a better estimation? - ANSWER Smaller (bigger n) Type I mistake - ANSWER Reject Ho when Ho is true Type II mistake - ANSWER Do not reject Ho when Ho is false Which is a sample statistic that is resistant to outlier? - ANSWER Sample IQR What distribution does a sampling distribution of the sample mean describe? - ANSWER The values of the sample mean from all