Exam 2 ISDS

With independent events, the multiplication rule simplifies to ...

P(A∩B)=P(A)P(B)

a bell curve

a normal curve is also called ...

event

a subset of the sample space

a statistic used to calculate population parameter

estimator

a value of one equals

indefinite events

it is representative of the population we are trying to describe

What is a primary requirement of a good sample?

Given odds for event A occurring of "a to b," the probability of A is

a/a+b

Given odds against event A occurring of "a to b," the probability of A is

b/a+b

is characterized by uncountable values because it can take on any value within an interval

continuous random variable

A particular value of the estimator

estimate

mutually exclusive

events that do not share any common outcome of an experiment

number or houses a realtor sells in a month

example of discrete random variable

marginal probabilities

The values in the margins of the joint probability table, which provide the probability of each event separately.

that the sum or the average of a large number of independent observations from the same underlying distribution has an approximate normal distribution

the central limit theorem states

dependant

the occurrence of one is related to the probability of the occurrence of the other

how much the population varies from the normality

the sample size used to approximate the normal distribution depends on _______________

union

union of two events, denoted A∪B, is the event consisting of all outcomes in A or B.

average of squared differences from the mean

variance

constant; unknown

a parameter is ________, although its value may be ____________

empirical probability

a probability value based on observing the relative frequency with which an event occurs

when the objective is to reduce costs

cluster sampling is preferred

a subset of the population

sample

improves; increases

according to the CLT, the approximation steadily ________ as the number of observations ____________

the tendency of a sample statistic to systematically overestimate or underestimate a population parameter

bias

compliment

compliment of event A, denoted Ac, is the event consisting of all outcomes in the sample space S that are not in A.

the weighted value of all possible values of a random variable

expected value

A sample space S yields eight equally likely events, E, F, G, H, I, J, K, and L. Find P(E U G U I).

(1/8+1/8+1/8) = .375

A sample space S yields eight equally likely events, E, F, G, H, I, J, K, and L. Find P(F^c)

(7/8 = e+g+h+i+j+k+l/e+f+g+h+i+J+k+l) = .875

an estimator

When a sample statistic is used to make inferences about a population parameter it is referred to as _______________

joint probability table

A contingency table whose frequencies have been converted to relative frequencies.

statistical inference

A major portion of statistics is concerned with __________ __________, where we examine the problem of estimating population parameters or testing hypotheses about such parameters.

bias

If a sample statistic continuously over-or-under estimates a population parameter then there is ________

the population mean μ and the population variance σ2

If the normal distribution is completely described by two parameters, what are the two parameters?

observations from each group

In stratified sampling, the sample consists of

two events, A and B, are independent if ...

P(A | B)=P(A)

when the objective is to increase precision

Stratified sampling is preferred

to increase precision

Stratified sampling is the preferred sample method when the objective is _________

If P(A) denotes the probability of an event A occurring, and P(A) does not equal zero or one, then:

The odds for A occurring equalP(A)/1−P(A), and The odds against A occurring equal1−P(A)/P(A)

joint probabilities

The values in the interior of the table represent the probabilities of the intersection of two events

independant

the occurrence of one event does not affect the probability of the occurrence of the other event

np is greater than or equal to 5 and n(1-p) is greater than or equal to 5

for any population proportion p, the sampling distribution of the sample proportion is approx. normally distributed if __________

observations from the selected groups

in cluster sampling, the sample consists of

intersection

intersection of two events, denoted A∩B, is the event consisting of all outcomes in A and B.

x=μ+zσ

inverse transformation formula

a simple event consists of:

just one of the possible outcomes of an experiment

a function of the random sample used to make inferences about the value of an unknown population parameter

point estimator

consists of all items of interest in a statistical problem

population

assumes a countable number of distinct values

discrete random variable

the waiting time at a toll booth

examples of continuous random variable

Two defining properties of probability

1. The probability of any event A is a value between 0 and 1; that is, 0≤P(A)≤1.0≤PA≤1. 2. The sum of the probabilities of any list of mutually exclusive and exhaustive events equals 1.

A sample space S yields eight equally likely events, E, F, G, H, I, J, K, and L.a. Find P(H).

(1/8 = h/e+f+g+i+j+k+l) = .125

Given two events A and B, each with a positive probability of occurring, the probability that A occurs given that B has occurred (A conditioned on B) is equal to

P(A | B)=P(A∩B)/P(B)

the probability that B occurs given that A has occurred (B conditioned on A) is equal to

P(B | A)=P(A∩B)/P(A)

False

True or False: The expected value of the sample proportion is not equal to the population proportion

True

True or False: the sample proportion is an unbiased estimator of the population proportion.

statistic; parameter

We use a calculated sample _______, to make inferences about an unknown population __________.

Probability

a numerical value that measures the likelihood that an event occurs

subjective probability

a probability value based on personal and subjective judgement

experiment

a process that leads to one of several possible outcomes. The diversity of the outcomes of an experiment is due to the uncertainty of the real world

the probability of interest is usually what type of probability?

conditional

sample space

contains all possible outcomes of the experiment

Heights and weights of newborn babies Scores on the SAT Cumulative debt of college graduates Advertising expenditure of firms Rate of return on an investment

examples of random variables that follow a normal distribution

The mean, the median, and the mode are all equal for a normally distributed random variable

if the normal distribution is bell shaped and symmetric around its mean, what happens with the mean median and mode?

a value of zero equals

impossible events

refers to a systematic difference in preferences between respondents and nonrespondents to a survey or a poll.

nonresponse bias

the most extensively used probability distribution in statistical work

normal probability distribution

Classical Probability

often used in games of chance; They are based on the assumption that all outcomes of an experiment are equally likely.

a function that assigns numerical values to the outcomes of an experiment

random variable

a random variable used to estimate the unknown population parameter of interest

sample statistic / statistic

the probability distribution of the sample mean

sampling distribution

refers to a systematic underrepresentation of certain groups from consideration for the sample.

selection bias

contingency table

shows frequencies for two qualitative (categorical) variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values.

a sample of n observations that has the same probability of being selected from the population as any other sample of n observations

simple random sample

a special case of the normal distribution with a mean equal to zero and a standard deviation (or variance) equal to one

standard normal distribution

compliment rule

states that the probability of the complement of an event, P(Ac), is equal to one minus the probability of the event; that is, P(Ac)=1−P(A).

addition rule

states that the probability that A or B occurs, or that at least one of these events occurs, is equal to the probability that A occurs, plus the probability that B occurs, minus the probability that both A and B occur. P(A∪B)=P(A)+P(B)−P(A∩B).

the population is first divided up into mutually exclusive and collectively exhaustive groups, called strata. A stratified sample includes randomly selected observations from each stratum. The number of observations per stratum is proportional to the stratum's size in the population. The data for each stratum are eventually pooled.

stratified random sample

multiplication rule

the probability that A and B both occur in P(A∩B)=P(A | B)P(B)

If A and B are mutually exclusive events ...

then P(A∩B)=0PA∩B=0 and, therefore, the addition rule simplifies to P(A∪B)=P(A)+P(B).

bell-shaped and symmetric around its mean, completely described by two parameters, and asymptotic

three characteristics of a normal distribution:

exhausted

when all possible outcomes of an experiment is included in the events