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FINAL EXAM Review Sheet MATH 2600
You may (but are not required to) bring:
1. a graphing calculator (TI-84+ or equivalent),
2. two 8.5 inch by 11 inch sheets of paper with notes (informally called "cheat sheets")
Descriptive Statistics
From a data set (typically within MATH 2600, a data set will be “small” (size  30) for convenience)
Produce a stem-leaf plot or a histogram
Find the mean, median, midrange, mode, variance, standard deviation
Find the five number summary (min, Q1, median, Q3, max) ; <Interquartile Range IQR = Q3 - Q1>
Draw a box plot (box and whiskers plot) from this summary
Describe a distribution (shape, center, variation, "quarters" of data set)
Finding the values of particular measures of center and particular measures of variation
For a value,
measures of position (also known as measures of relative standing)
determine if this value is an outlier (what are the methods by which this is done?)
Apply
Chebyshev's Rule <for any distribution>
Empirical Rule <only appropriate for bell-shaped (mound-shaped) distributions>
Determine if an event is "common" or "uncommon"
typically use 2-standard deviations (sometimes 3 std deviations) from the mean as a measure
Probability
Determine the sample space of an experiment, Determine the complement of an event
Random Variables (the assignment of a real number to each object in the sample space)
Find theoretical probabilities under "equally likely" assumption
Determine if events are independent
(A and B are independent iff P(A and B) = P(A)P(B) or P(A|B)= P(A) or P(B|A) = P(B))
Addition rule P(A or B) = P(A) + P(B) – P(A and B), Multiplication rule P(A and B) = P(A|B)P(B)
Counting using addition rule, multiplication rule, combinations, permutations
Discrete probability distributions (discrete random variables, probability distribution function)
determining if a discrete probability distribution meets the relevant two requirements
mean (expected value) variancestandard deviation
Bernoulli trials, Binomial experiments, Binomial distribution: n, p, q, X, x, P(X = x),
Find probabilities of events of binomial experiments
P(X = x) = binompdf(n,p,x)
P(0  X  x) = binomcdf(n,p,x)
Continuous probability distributions (continuous random variables, probability density function)
uniform distribution
normal distribution ,X ~ N() ---- standard normal z ~ N()
x0 = invnorm(Area under the density function to the left of x0,)
P(Low  X  High) = normcdf(Low, High, )
Inferential Statistics
Central Limit Theorem -- Sampling Distributions for the sample mean
Confidence Intervals for a population mean
Using ZInterval or TInterval as appropriate, Interpretations
Hypothesis Tests for claims about the population mean (one-tailed, two-tailed)
Using ZTest or TTest as appropriate, test statistic, p-value, null hypothesis, alternate hypothesis
Interpretation in contextual application problems
Given an application problem, knowing how to interpret values found in terms of the application