Statistics Chapter 4

A ____________________ is the distribution of the number o successes in a string of Bernoulli Trials

binomial distribution

considers the possibility that the outcome will be less than or equal to a certain value

cumulative probability distribution

While individuals such as baseball statisticians are concerned solely with the organization and presentation of data

descriptive statistics

a random draw implies that the choice of one card carries the same chance as a choice of another.

equally likely

allows decision makers a way to order their judgments and present their assessment of the probabilities in an easily interpreted and useful form.

probability distributions

a probability distribution useful when there are a limited number of outcomes and the decision maker can assign probabilities to each of those outcomes.

probability mass function (PMF)

outcomes need to be mutually exclusive and collectively exhaustive, but they do not necessarily have to be equally likely (since each outcome is assigned its own probability which may be different from those of all the other outcomes).

probability theory

the ratio of the occurrence of a singular event and the total number of outcomes.

relative frequency method

collective term for the data points you are gathering

sample

the mean value of the characteristic we are studying in all of our samples, determined using the formula for the mean given in Chapter 2

sample mean

A quantitative technique that helps a user infer information about a general population based on data collected from one a small sample of the population

sampling theory

chart which states the probability of selling a certain number of cars each week

simple probability distribution.

The standard deviation,symbolized by the Greek lettersigma ( ), and the variance, which is the square of the standard deviation (^2), are measures of _______ or ______.

spread or dispersion

Defined as the square root of the sum of the squared difference between the data points and the mean multiplied by the probability of their occurence

standard deviation

level of uncertainty around the sample mean

standard error

The mode can be identified as the __________ on the CDF or the highest point on the probability mass function, signifying the outcome having the highest probability of occurring.

steepest point

When the weatherperson states that there is a 30% chance of showers, usually this has not been derived using any standard statistical measure of probability; rather, she is assessing the probability of rain, arrived at through intuition, knowledge, research and judgment. This is known as:

subjective probabilities

One can find the probability that the next trial or sample is above or below a certain point by translating that point into a z-score, AKA _____, and then looking up the z score in appendix c to determine the probability.

the number or standard deviations the point is away from the mean

a set of joints is collectively exhaustive if:

they encompass the entire range of possible outcomes

The median is also known as the

.5 fractile

Say that we are racing cars. Half of the cars are built by Speedy Motors and half are built by Zippy Carbuilders. Of the Speedy cars, half are red and half are yellow. Of the Zippy Cars, half are blue and half are red. There is an equal chance that any car will win. What is the probability that a red car will win?

0.5 (.5 x .5) + (.5 x .5) = .5 There is an equal probability that any car will win the race, so the probability of a red car winning is .5

In a deck of cards, what is the probability of randomly drawing the King of Clubs?(as a fraction)

1/52

There are 50 people in a room. The probability that a person in the room has brown hair is .80. Of these people with brown hair, 40% of them have brown eyes. How many people in the room have brown hair but do not have brown eyes?

24. Multiply the .80 probability of having brown hair by the (1-0.40?=.60 probability of brown haired people not having brown eyes to get the probability of anyone in the room having brown hair, but not brown eyes. Then multiply by 50 to determine the number of people this includes.

Suppose we have a normal distribution with a mean of 225 and a standard deviation of 30. Suppose that z-score for the next sample is 2.5. What is the sample value?

300. Take (x-225)/30=2.5 & solve for x.

____________ are characterized by measures of their centers and their dispersion, or how spread out potential outcomes are

Probability Distributions

All possibilityes should add up to 1 or 100%

Probability Mass Function

As children, most of us learned that the probability of rolling a 3 on a six-sided die is 1/6, since only one side of the die has three spots. This is an example of:

Simple Theoretical Probability

T/F The mode of a probability is the most likely outcome.

TRUE.

T/F Z-score is (plus or minus) the number of standard deviations that an observation is away from the mean.

TRUE.

T/F A distribution that is not a normal distribution still has a standard deviation

TRUE. Probability distributions still have standard deviations.

T/F Standard deviation is a measure of spread or dispersion.

TRUE. Standard deviation is used to measure the points around the mean of these points.

T/F The mean, median, and mode are all the same in a normal distribution

TRUE. The mean of a normal distribution is also the media, since half of the data points fall on each side. The mean is also the most likely outcome (the outcome having the highest probability of occuring, which is why it sits atop the bell-shaped normal curve; this the mean is the mode, as well.

T/F The type of probability described in the statement "the probability of a randomly selected person having brown hair is 80% if it is a woman" is a conditional probability

TRUE. joint probability of two events occurring together, while conditional probability is the probability of one event occurring conditional upon another that is already known or has already occurred.

A __________________is an event that has two possible outcomes: one a success, the other a failure. (ex: flipping a coin)

Bernoulli Trial

If a situation can result in y possible outcomes, and x of these are termed successes, then the probability of a success is x/y. What is this probability?

Classic Probability Theory

measures the likelihood of something happening, but in a classic sense, it also means that every statistical experiment will contain elements that are equally likely to happen.

Classic Probability Theory

s the probability of one event occurring conditional upon another that is already known or has already occurred.

Conditional probability

T/F A Bernoulli Trial is an event with two or more possible outcomes

FALSE. A bernoulli trial is an event with ONLY two possible outcomes.

the probability of two events occurring together. for example, an ace that is a spade

Joint probability

you take data from samples and make generalizations about a population.

inferential statistics

shows how confident we are that the true mean is within a certain range around the sample mean.

interval estimates

A normal distribution can be described by its ______ and __________.

mean, standard deviation

The _________, divides the distribution into two equally likely areas.

median

The _______, another measure of the center of the distribution, is the most likely outcome

mode

(there are no duplicate outcomes as long as cards already drawn are not put back in the deck

mutually exclusive

This distribution is probably the widest known and most useful distribution in statistics.

normal curve

The probability distribution for a number of random variables is a bell-shaped curve called the _______

normal curve.

best used when each data point represents a sum or average of some other bits of data, in order to allow the user to infer something about this greater whole.

normal distribution

the total collection of objects or people to be studied, from which a sample is to be drawn

population

the mean value of that characteristic in all of the objects or people in the population

population mean (true mean)

To measure the center of a __________________, you can find its mean or expected value, designated by the Greek letter mu (μ).

probability distribution