Statistics Exam 2 Definitions (Ch 4, 5, 6)

Which type of compound event is generally associated with​ multiplication? Which is generally associated with​ addition?

An AND compound event is generally associated with​ multiplication; an OR compound event is generally associated with addition.

In​ probability, a(n)​ ________ is any process that can be repeated in which the results are uncertain.

experiment

Two variables that are linearly related are _________________ when above-average values of one variable are associated with below-average values of the other variable. That is, two variables are negatively associated if, whenever the value of one variable increases, the value of the other variable decreases.

negatively associated

Two variables that are linearly related are ________________ when above-average values of one variable are associated with above-average values of the other variable (or below-average values of one variable are associated with below-average values of the other variable). That is, two variables are positively associated if, whenever the value of one variable increases, the value of the other variable also increases.

positively associated

The _______________ of a discrete random variable X provides the possible values of the random variable and their corresponding probabilities. A probability distribution can be in the form of a table, graph, or mathematical formula.

probability distribution

A ______________ is a numerical measure of the outcome of a probability experiment; so its value is determined by chance.

random variable

A​ _______ is a scatter diagram with the residuals on the vertical axis and the explanatory variable on the horizontal axis.

residual plot

The ______________, S, of a probability experiment is the collection of all possible outcomes for that experiment.

sample space

Describe what an unusual event is. Should the same cutoff always be used to identify unusual​ events? Why or why​ not?

An event is unusual if it has a low probability of occurring. The same cutoff should not always be used to identify unusual events. Selecting a cutoff is subjective and should take into account the consequences of incorrectly identifying an event as unusual.

Describe how the value of n affects the shape of the binomial probability histogram.

As n​ increases, the binomial distribution becomes more bell shaped.

What is the formula for the expected number of successes in a binomial experiment with n trials and probability of success​ p?

E(X)=np

A binomial experiment is performed a fixed number of times. What is each repetition of the experiment​ called?

Each repetition of the experiment is called a trial.

What method of assigning probabilities to a simple event uses relative​ frequencies?

Empirical

State the criteria for a binomial probability experiment.

The trials are independent. Each trial has two possible mutually exclusive​ outcomes: success and failure. The probability of​ success, p, remains constant for each trial of the experiment. The experiment consists of a fixed​ number, n, of trials.

What does it mean to say that two variables are positively​ associated?

There is a linear relationship between the​ variables, and whenever the value of one variable​ increases, the value of the other variable increases.

Total deviationequals=​_______ deviationplus+​_______ deviation

Total deviationequals=unexplained deviationplus+explained deviation

Determine if the following statement is true or false. Probability is a measure of the likelihood of a random phenomenon or chance behavior.

True

Determine if the following statement is true or false. In the binomial probability distribution​ function, nCx represents the number of ways of obtaining x successes in n trials.

True

Is the statement below true or​ false? The​ least-squares regression line always travels through the point (xbar,ybar)

True

True or False​: In a probability​ model, the sum of the probabilities of all outcomes must equal 1.

True

The __________________ is a discrete probability distribution that describes probabilities for experiments in which there are two mutually exclusive (disjoint) outcomes.

binomial probability distribution

The _______________, R2, measures the proportion of total variation in the response variable that is explained by the least-squares regression line.

coefficient of determination

The​ _______, Upper R squaredR2​, measures the proportion of total variation in the response variable that is explained by the least squares regression line.

coefficient of determination

A _______________ is a collection, without regard to order, in which r objects are chosen from n distinct objects with r≤n without repetition. The symbol nCr represents the number of combinations of n distinct objects taken r at a time.

combination

A ________________ lists the relative frequency of each category of the response variable, given a specific value of the explanatory variable in the contingency table.

conditional distribution

A ________________ has either a finite or countable number of values. The values of a discrete random variable can be plotted on a number line with space between each point.

discrete random variable

The __________________, or Pearson product moment correlation coefficient, is a measure of the strength and direction of the linear relation between two quantitative variables. The Greek letter ρ (rho) represents the population correlation coefficient, and r represents the sample correlation coefficient. We present only the formula for the sample correlation coefficient.

linear correlation coefficient

A ________________ of a variable is a frequency or relative frequency distribution of either the row or column variable in the contingency table.

marginal distribution

A ______________ is an ordered arrangement in which r objects are chosen from n distinct (different) objects so that r≤n and repetition is not allowed. The symbol nPr represents the number of permutations of r objects selected from n objects.

permutation

A _____________ is a graph that shows the relationship between two quantitative variables measured on the same individual. Each individual in the data set is represented by a point in the scatter diagram. The explanatory variable is plotted on the horizontal axis, and the response variable is plotted on the vertical axis.

scatter diagram

A _______________ is a probability that is determined based on personal judgment.

subjective probability

An _______________ is an event that has a low probability of occurring.

unusual event

What is meant by a conditional​ distribution?

A conditional distribution lists the relative frequency of each category of the response​ variable, given a specific value of the explanatory variable in a contingency table.

What is meant by a marginal​ distribution?

A marginal distribution is a frequency or relative frequency distribution of either the row or column variable in a contingency table.

What is a random​ variable?

A random variable is a numerical measure of the outcome of a probability experiment.

What is a​ residual? What does it mean when a residual is​ positive?

A residual is the difference between an observed value of the response variable y and the predicted value of y. If it is​ positive, then the observed value is greater than the predicted value.

The notation P(F|E) means the probability of event_______given event________.

F, E

True or​ false: Correlation implies causation.

False

If the linear correlation between two variables is​ negative, what can be said about the slope of the regression​ line?

Negative

What does it mean if r=​0?

No linear relationship exists between the variables.

If E and F are disjoint​ events, then P(E or F)=

P(E)+P(F)

If E and F are not disjoint​ events, then​ P(E or ​F)=​________.

P(E)+P(F) - P(E and F)

State the conditions required for a random variable X to follow a Poisson process.

The probability of two or more successes in any sufficiently small subinterval is 0. The number of successes in any interval is independent of the number of successes in any other interval provided the intervals are not overlapping. The probability of success is the same for any two intervals of equal length.