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Stat 503 final exam.pdf, Exams of Statistics

Boston City CampusStatistics

Stat 503 final exam.pdf Stat 503 final exam.pdf

Typology: Exams

2024/2025

Available from 07/01/2025

jacob-kenyatta
jacob-kenyatta 🇿🇦

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Download Stat 503 final exam.pdf and more Exams Statistics in PDF only on Docsity!

STAT 503 FINAL EXAM (ACTUAL 2025) SOLVED CORRECT ANSWERS. Is a quantitative variable always measured in numbers? - <<>>Yes Is any measurement that you record from a sample a variable? - <<>>False What is a statistic? - <<>>The measure that is taken from the whole sample as a summary of the sample What is the Xbar - <<>>Sampling distribution of sample mean Central Limit Theorem requirements - <<>>Sample size greater than 25 OR Population distribution is normal CLT set-up - <<>>Xbar~Normal(1, o/sqrt(n)) How to calculate margin of error (ME) - <<>>Za/2, o/sqrt(n) What is the margin of error - <<>>The width of the confidence interval that you can build on possible sample means so that 1-a (success rate) of them would contain u The smaller CI, the... ... ME - <<>>Smaller ME The larger n is, the ... ... ME - <<>>Smaller ME Z-method assumptions - <<>>N is > 25 or X~N(iL, 0) 6 is known Z-method equation - <<>>Xbar +/- z(o/sqrt(N)) T-method assumptions - <<>>N is > 25 or X~N(uL, 9) o is unknown T-method equation - <<>>Xbar +/- t(df)(s/sqrt(n)) What is included in a box plot summary? - <<>>Q0 = minimum Q1 = median of lower half Q2 = median Q3 = median of upper half Q5 = maximum What is the the interquartile range (IQR)? - <<>>Q3 - Q1 (shown inside box plot) What is an outlier? - <<>>Any data that is Q3 + 1.5IQR or Q1 - 1.5 IQR When is a phenomenon random? - <<>>When it has uncertain outcomes in a short run (sample) but show regular distribution in a long run (population) What is an outcome? - <<>>Observation of a variable What is a probability model? - <<>>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) - <<>>P(AB) = P(A) P(B|A) = P(B) P(AIB) What is the addition rule? (disjoint) - <<>>P(A or B) = P(A) + P(B) - P(AB) If A and B are disjoint, the must be dependent. - <<>>TRUE Why is a probability tree diagram used? - <<>>To show multiple variables according to stages (the order that they happen) What is written on each segment in a probability tree? - <<>>A conditional probability What probability is at the end of the branch on a probability tree? - <<>>The product of the probabilities of the segments of that branch What are all ultimate outcomes of probability tree? - <<>>Disjoint outcomes, non-overlapping "Sensitivity" (HIV example) - <<>>P(T+| HIV+) Compute Var(X-Y) - <<>>0“2(1) + o%2(2) or (202) Compute Var(X+Y/2) - <<>>(0“2(1) + 0%2(2))/4 How to denote a binomial variable - <<>>X~Bin(n, p) (n is the sample size, p is the constant proportion of success) What is X defined as in a binomial - <<>>The number of successes Mean of binomial variable - <<>>np Standard deviation of binomial variable - <<>>sqrt(np(1-p)) Effect of changing p - <<>>Small p (0.05) is skewed right Mid p (0.5) is symmetric Large (0.95) is skewed left Effect of increasing n - <<>>Distribution becomes more bell-shaped Normal approximation to the binomial - <<>>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... - <<>>Within | standard deviation from the mean Bell shape rule - 95% of values are... - <<>>Within 2 standard deviations from the mean Bell shape rule - 99.7% of values are... - <<>>Within 3 standard deviations from the mean Standardize using z-score - <<>>X - p/o When does X approximately follow the normal approximation to binomial? - <<>>When np and np(1-p) are both >10 What distribution does a sampling distribution of the sample mean describe? - <<>>The values of the sample mean from all possible samples