Stats Exam 2

normal probability distribution

- symmetrical about mean, bellshaped, - mean=median=mode, - asymtotic to x-axis, - location is determined by mean and standard deviation, - probability is area under the curve, total area under the curve=1, P(x-a) = 0 = (1/infinity),

The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is ______.

1/(b - a) between a and b, and zero otherwise

How many parameters are needed to fully describe any normal distribution?

2

stratified random sampling

A form of probability sampling; a random sampling technique in which the researcher identifies particular demographic categories of interest and then randomly selects individuals within each category.

standard normal distribution

A normal distribution with a mean of 0 and a standard deviation of 1.

simple event

One outcome for an event.

An event is independent if

P(A I B) = P(A)

nonresponse bias

a systematic difference in preferences between respondents and non-respondents

contingency table

a table that shows frequencies for two qualitative variables

continuous uniform distribution

defined over a range that spans between some lower limit, a, and some upper limit b, which serves as the parameters of the distribution.

Statistics are used to estimate population parameters, particularly when it is impossible or too expensive to poll an entire population. A particular value of a statistic is referred to as a(n) ______.

estimate

intersection

event consisting of all outcomes in A AND B.

Union

event consisting of all outcomes in A or B; AuB

mutually exclusive

events that cannot happen at the same time

Events are exhaustive if they do not share common outcomes of a sample space.

false (Events are exhaustive if they include all outcomes in the sample space.)

Two events A and B are independent if the probability of one does not influence the probability of the other.

true

exponential probability distribution

used to describe the time it takes between occurences of an event

Total Probability Rule

used to determine the unconditional probability of an event, given conditional probabilities

Classical Probability

used when each outcome in a sample space is equally likely to occur

Bayes' theorem uses the total probability rule to update the prior probability of an event that has not been affected by any new evidence.

False (Bayes' theorem is a procedure for updating prior probabilities based on new information.)

A continuous random variable has the uniform distribution on the interval [a, b] if its probability density function f(x) ______.

Is constant for all x between a and b, and 0 otherwise

empirical probability

Observed relative frequency with which an event occurs (experiment must be repeated a lot of times to get empirical probability)

Bayes' Theorem

Used to update prior probabilities with new information

joint probability table

a contingency table whose frequencies have been converted to relative frequencies

Probability

a numerical value that measures the likelihood that an event occurs

selection bias

a systematic underrepresentation of certain groups from consideration for a sample

marginal probabilities

probabilities of each event separately

experiment

process that leads to one of several possible outcomes

bias

tendency of a sample statistic to systematically overestimate or underestimate a population parameter. Often caused by samples who do not represent the population

Law of Large Numbers

the empirical probability approaches the classical probability if the experiment is run a very large number of times

subjective probability

the individual's personal estimate of the chance of loss

Conditional Probability

the probability of an event is conditional on the occurrence of another event

Complement Rule

the probability of an event occurring is 1 minus the probability that it doesn't occur

Joint Probability

the probability of the intersection of two events

multiplication rule

the probability that A AND B occur

addition rule

the probability that either A or B occurs, or that at least one of these events occurs

sample space

the set of all possible outcomes

Bias can occur in sampling. Bias refers to ______

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

social desirability bias

the tendency to respond to questions in a socially desirable manner, instead of giving a real answer

In an experiment in which a coin is tossed twice, which of the following represents mutually exclusive and collectively exhaustive events?

{TT, HH} and {TH, HT}

Probabilities can be expressed as fractions, percentages, and _______

odds

combination formula

order does not matter

Permutation Formula

order matters

complement

outcomes that are not included in that

Which of the following meets the requirements of a stratified random sample?

A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include two people chosen at random under the age of 25 and four people chosen at random over 25.

Let X be normally distributed with mean μ and standard deviation σ > 0. Which of the following is true about the z value corresponding to a given x value?

A positive z = (x - μ)/σ indicates how many standard deviations x is above μ. A negative z = (x - μ)/σ indicates how many standard deviations x is below μ. The z value corresponding to x = μ is zero. All of the above.

cluster sampling

A probability sampling technique in which clusters of participants within the population of interest are selected at random, followed by data collection from all individuals in each cluster.

simple random sample

A sample of size n selected from the population in such a way that each possible sample of size n has an equal chance of being selected.

event

A subset of a sample space.

exhaustive

including all possible outcomes in sample space

The central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the sample mean ______.

is closer to a normal distribution

Using the central limit theorem, applied to the sampling distribution of the sample proportion, what conditions must be met?

np≥5 and n(1−p ) ≥ 5

Probabilities can be expressed as fractions, percentages, and ______.

odds