ST 260 Exam 2 Casselman

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compute to z values

(score-mean)/standard deviation

expected value formula

(x* the probability) summed up

conditions of a binomial distribution

1) a fixed number of trials "n" 2) all n trials must be independent of each other 3) all same probability of success on each trial 4)x= count of the number of successes

areas between standard deviations

68,95,99.7

statistics

the science of decision making in the face of uncertainty

independence

two events are independent if one event does not affect the probability of another event

Bernoulli distriution

a discrete data distribution used to describe a population of binary variable values

binomial distribution

a discrete data distribution used to model a population of counts for "n" independent repetitions of a Bernoulli experiment

probability

a numerical measure of the likelihood that an event will occur

expected value

an experiment repeated many times and the average of the result

quantitative variables

averages or differences have meaning

continuous random variable

can assume any value in an interval on the real line or in a collection of intervals

three methods for assessing probability

classical, relative frequency, subjective

categorical variables

classify people or things

normal probability distribution standard deviation

determines width of the curve- larger deviation results in wider and flatter curves

statistical inference

generalizing from a sample to a population, by using a statistic to estimate a parameter

sampling distribution of x

is the distribution of all possible sample means calculated from all possible samples of size n also called the population of all possible x bars

pi=

mean

standard normal distribution

mean =0 and standard deviation=1

bigger variance=

more risk

probability requirements for discrete variables

must be between zero and 1 P(A)=0 imposible P(A)=1 certain sum up probabilities of all possible outcomes must equal 1

mean of a binomial distribution

n(pi)

z=

number of standard deviations that an x value is from the mean

a fair bet

one in which the expected value of the winnings is zero (don't pay more than the expected value)

binary

only one of two outcomes can occur (0 and 1)

p(a and b)

p(a)*p(b|a)

p(a or b)

p(a)+p(b)-p(a and b)

sample proportion variance

pi(1-pi)/n

confidence interval

point estimate +/- margin of error

if the true population standard deviation is known

replace sigma with s replace z with t

standard error of a sampling distribution

sigma/sqrt(n)

standard deviation

sqrt(npi(1-pi))

standard deviation of bernoulli

sqrt(pi(1-pi))

standard deviation expected value

square root of variance

variance expected value

sum of (x-expected value)^2 *p

as n-1 increases

t sub n-1 approaches z

conditional probability

the chance one event will happen given another event will occur p(a and b)/p(b)


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