Statistics Test 2 Flashcards

Questions and Answers

What is the difference between theoretical probability and empirical probability?

Empirical probability tells us how often an event occurs in an actual set of experiments or observations. Theoretical probabilities are based on theory telling us about events that occur indefinitely.

What does the Law of Large Numbers state?

The larger the number of individuals that are randomly drawn from a population, the more representative the resulting group will be of the entire population.

What are mutually exclusive events?

Events that cannot happen at the same time.

What are examples of mutually exclusive events?

Turning left and turning right, getting heads and tails. Signup and view all the answers

Probability is used to _____________.

measure how often random events occur. Signup and view all the answers

What is theoretical probability?

Long run relative frequencies. Signup and view all the answers

What is empirical probability?

Relative frequencies based on an experiment or observation. Signup and view all the answers

Probability is always a value between it may appear as a .

0-1- fraction-decimal or percent. Signup and view all the answers

If p(A) is 1, the event is certain to occur.

True Signup and view all the answers

If p(A) is 0, the event is certain not to occur.

True Signup and view all the answers

What are unusual events?

Events that occur less than 5% of the time. Signup and view all the answers

What does the complement rule state?

P(A^c) = 1 - P(A). Signup and view all the answers

What is the addition rule of mutually exclusive events?

P(A or B) = P(A) + P(B). Signup and view all the answers

What is the addition rule for not mutually exclusive events?

P(A or B) = P(A) + P(B) - P(A and B). Signup and view all the answers

For dependent events, what is the formula for conditional probability?

P(A and B) P(B/A) = P(A). Signup and view all the answers

In which context is the word 'given' used?

Conditional probabilities. Signup and view all the answers

In which context is the word 'or' used?

Independent events. Signup and view all the answers

What are independent events?

P(A or B) = P(A) + P(B). Signup and view all the answers

What is a permutation?

The number of permutations of R objects chosen from n. Signup and view all the answers

In permutations, what is the significance of order?

Important. Signup and view all the answers

In combinations, what is the significance of order?

Not important. Signup and view all the answers

How do you find the area to the right in a standard normal distribution curve?

Locate the number on the z chart; this is the area to the left; must subtract 1 to find the area to the right. Signup and view all the answers

How to find the area between in a normal distribution curve?

Locate the area on the z chart and subtract the big from the small. Signup and view all the answers

How to find the z score when given area to the right or to the left?

Find the closest number and then find the corresponding closest z score; when locating area to the right, subtract one from the given area. Signup and view all the answers

In what context are area, proportion, and probability considered the same?

Normal distribution. Signup and view all the answers

What is the z score of x?

Score - mean divided by standard deviation. Signup and view all the answers

When looking for an area that is greater, which direction are we looking?

Right. Signup and view all the answers

To find the area to the right, what must we subtract?

Because the z chart shows areas to the left. Signup and view all the answers

How do we find the value if we know the mean, standard deviation, and z score?

Convert percentage into z score by finding the closest corresponding number; use it in the formula x = mean + (z multiplied by standard deviation). Signup and view all the answers

What does the Central Limit Theorem state?

The sampling distribution of the mean will approach the normal distribution as n increases (n > 30). Signup and view all the answers

What is the formula for the Central Limit Theorem?

x minus mean divided by the square root of the sample. Signup and view all the answers

Study Notes

Probability Concepts

Theoretical Probability: Derived from theoretical understanding, indicating long-run relative frequencies of events.
Empirical Probability: Based on actual experiments or observations, showing how often an event occurs in practice.
Probability values range between 0 (impossible event) and 1 (certain event); can be expressed as a fraction, decimal, or percentage.

Rules of Probability

Law of Large Numbers: Sample sizes increase, results become more representative of the population's true probabilities.
Complement Rule: P(A^c) = 1 - P(A); the probability of an event not occurring is equal to one minus the probability it will occur.
Addition Rule for Mutually Exclusive Events: P(A or B) = P(A) + P(B); for events that cannot happen simultaneously.
Addition Rule (Not Mutually Exclusive): P(A or B) = P(A) + P(B) - P(A and B) applies when events can occur together.

Types of Events

Mutually Exclusive Events: Events like turning left or right, or getting heads or tails, cannot occur at the same time.
Independent Events: Events where the occurrence of one does not affect the other, calculated as P(A or B) = P(A) + P(B).
Dependent Events: The occurrence of one event depends on another; use P(A and B) with P(B/A) for calculations.

Unusual Events

Defined as events happening less than 5% of the time, indicating rarity.

Statistical Measures

Z Score: Calculated as (score - mean) / standard deviation; indicates the number of standard deviations an observation is from the mean.
Area proportions in normal distribution are equivalent to probabilities; finding areas involves using Z scores and charts.

Sampling and Distribution

Central Limit Theorem: As sample size (n) increases (n > 30), the sampling distribution of the mean approaches a normal distribution.
Finding areas in standard normal distributions requires reference to Z charts; to find the area to the right, subtract the area from 1.

Permutations and Combinations

Permutation: The arrangement or ordering of R objects chosen from a total of n, where order is significant.
Combination: Selection of R objects from n where order does not matter, focusing on the grouping rather than arrangement.

Finding Areas and Values

To find the area between two Z scores, look up each score, subtract the smaller area from the larger for the final value.
To find associated values given the mean and standard deviation, use the formula x = mean + (z * standard deviation).

Summary

Probability theories and rules form the foundation of understanding random events and their behaviors.
Becoming proficient in calculating and interpreting probabilities enhances comprehension in statistics.

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Explore key concepts in statistics with these flashcards, focusing on the difference between theoretical and empirical probability, as well as the Law of Large Numbers. Perfect for preparing for your upcoming statistics test.