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, partitions

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