stats exam 2

z-score

represents the distance that a data value is from the mean in terms of the number of standard deviations

response variable

variable whose value can be explained by the value of the explanatory variable or predictor variable

scatter diagram

graph that shows the relationship between two quantitative variables measured on the same individual

on what axis is the explanatory variable plotted

x

on what axis is the response variable plotted

y

two variables that are linearly related are _________________________ when above average values of one variable are associated with above average values of the other variable and below average values of one variable are associated with below average values of the other variable

positively associated

two variables that are linearly related are _________________________ when above average values of one variable are associated with below average values of the other variable

negatively associated

linear correlation coefficient

measure of the strength and direction of the linear relation between two quantitative variables

residual

the observed distance between the observed and predicted value of y

least squares regression line

line that minimizes the sum of the squared errors or residuals

law of large numbers

as the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the probability of the outcome

sample spaces (s)

collection of all possible outcomes

event

any collection of outcomes from a probability experiment; consists of one outcome or more than one outcome

simple event

an event with one outcome

rules of probabilities

1. the probability of any event E, P(E), must be greater than or equal to 0 and less than or equal to 1

2. the sum of the probabilities of all outcomes must equal 1

probability model

lists the possible outcomes of a probability experiment and each outcome's probability

impossible event

probability is 0

certainty event

probability is 1

random variable

a numerical measurement of the outcome of a probability experiment, so it's value is determined by chance

discrete random variable

has either a finite or countable number of values that can be plotted on a number line with space between each point

continuous random variable

has infinitely many values that can be plotted on a line in an uninterrupted fashion

mean of a random variable

represents what we would expect to happen in the long run; also called the expected value

expected value

mean of a random variable

binomial probability experiment criteria

1. experiment is performed a fixed number of times. each repetition is called a trial.

2. trials are independent, outcomes don't affect each other

3. two mutually exclusive outcomes for each trial are success and failure

4. probability of success is the same for each trial of the experiment

what is each repetition called

trial

trials are ______________

independent

two mutually exclusive outcomes of each trial

success and failure

probability of success is ____________________ for each trial of the experiment

the same

binomial random variable

x is a random variable which represents the number of successes in n trials of a binomial experiment

notation used in binomial probability distribution

1. There are n independent trials of the experiment.

2. P denotes the probability of success for each trial so that 1-p is the probability of failure for each trial.

3. X denotes the number of successes in n independent trials of the experiment. 0 ≤ x ≤ 1.

in binomial probability distributions, there are ____ independence trials of the experiment

n

cumulative distribution function (cdf)

computes probabilities less than or equal to a specified value

probability density function (pdf)

an equation used to compute probabilities of continuous random variables

probability density functions must satisfy the two following properties:

1. the total area under the graph of the equation over all possible values of the random variable must equal 1

2. the height of the graph of the equation must be greater than it equal to 0 for all possible values of the random variable

a continuous random variable is _, or has a ____, if its relative frequency histogram has the shape of a normal curve

normally distributed, normal probability distribution

properties of the normal density curve

1. It is symmetric about its mean

2. Because mean = median = mode, the curve has a single peak

3. It has inflection points at 1 standard deviation of the mean

4. The area under the curve is 1

5. The area under the curve to the right of the mean and the area under the curve to the left of the mean both equal .5

6. As x increases and decreases, the graph approaches but never reaches the horizontal axis.

7. The Empirical rule applies