Stats - Exam 3

random phenomena example

trial: flipping of three coins, Outcome: heads or tails for each flip, Event: heads, tails, heads, Sample space: (HHH, HHT, HTH…)

law of large numbers

as the number of trials increases, the proportion of times an event occurs settles down to one number that is the probability of the event

identical probabilities

the probabilities for each event must remain the same for each trial

independence

the outcomes of the previous trials don’t influence the outcome of a trial

empirical probability

the ratio of the number of outcomes in which a specified event occurs to the total number of trials, not in a theoretical sample but in an actual experiment

theoretical probability

when we have equally likely outcomes we write the probability of event A as # of outcomes in A/ total # of outcomes possible

personal probability

a number between 0 and 1 based upon personal views concerning whether the event will occur or not

formal probability rules

between 0 and 1; probability assignment rule, s is a sample space; let a be any event and Ac is its complement; let a and b be two disjoint events; let a and b be two independent events

conditional probability

measures the probability of an event given that another event has occured; probability of a given b

disjoing; independent

_______ event cannot occur simultaneously. Disjoing events are never _______

sampling distribution of a proportion

the distribution of all possible sample proportions from samples with the same sample size

sampling distribution for porportions

symmetric, unimodal, centered at p and the sampling distribution follows the normal model when conditions are met

normal model rules

independence, must be independent of each other; 10% condition, sample size n shouldn’t be larger than 10% of the population; success/failure, enough # of successes and failures

sampling distribution tells us…

allows us to make statements about the location of the corresponding population parameter and the precision of these statements

standard error

whe we estimate the standard deviation of a sampling distribution this is the SE; it’s not an error since no error has been made; it’s the variation from sample to sample

fixed

population proportion is ______

interpreting confidence level

we are x confident that between x and x of all clients will not make timely payments.

formal interpretation

about x of samples of this sample size will produce confidence intervals that capture the true proportion

margin of error

the extent that interval on either side of P^ is called this;

short; high

_____ confidence interval with a ____ confidence level is preferable

change the confidence level

we need to change the number of SEs so that the size of the margin of error corresponds to the new level; critical value

central limit theorum

sequence of independent random variables; the larger the sample the better; the CLT explains why means tend to behave normal; we don’t know sigma and mu so we use y bar and s to estimate them

distribution is normal…

when there’s a large sample size and population is close to normal

degrees of freedom

represent the # of independent values in a sample that are free to vary when estimating a statistical parameter like the mean

student t-models

unimodal, symmetrical, and bell-shaped like the normal model; only a few degrees of freedom have a shorter peak than the normal model and fatter tails; as the degree increases the t-models look more and more like normal models

confidence level; degrees of freedom

critical value depends on the _____ _____ and the _______ __ _______

t-level conditions

independence, data should be from a random sample/randomized process and observations should be independent; nearly normal, pop. distribution should be normal or the sample size should be large;

small; no strong

for ____ samples the data should show ________ skewness or outliers

large; robust; departures

for _____ samples the t interval is _____ to moderate _____ from normality