Statistics and Probability Concepts

These flashcards cover key concepts in statistics and probability, aiding in exam preparation.

What is a Continuous Variable?

A variable with a wide and infinite number of values (e.g., age, test scores, height).

What are Discrete Variables?

Variables that have a countable amount of values (e.g., test scores on a scale of 1-10, no decimals).

What is Interval-Level Data?

Data with a defined unit of measure, no true zero point, and equal intervals between successive values (e.g., temperature, dress size).

Define Ratio-Level Data.

Data with a defined unit of measure, a real zero point, and equal intervals between successive values with no negatives (e.g., money, age, duration).

What is Nominal-Level Data?

Classifications of groups or categories that measure data by name only and are mutually exclusive (e.g., race, sex, zip code, car model).

What is Ordinal-Level Data?

Data that is ranked in order but does not have precise differences between ranks (e.g., rank in class).

What is a Normal Distribution?

A distribution where mode, median, and mean are all equal.

Describe a Positively Skewed Distribution.

A distribution where mode < median < mean.

What is an Ordered Array?

Organized data focusing on major features or data placed in rank order.

What is a Stem-and-Leaf Display?

A way to display data by dividing each observation into a stem value and a leaf value.

Define Frequency Distribution.

A list or table containing the values of a variable and the corresponding frequencies for each value.

What is Discrete Data?

Data where possible values are countable.

What is Relative Frequency?

The proportion of each category within a distribution.

What is Continuous Data?

Data that may take on any value within some interval.

What is Chebyshev's Theorem?

An estimation of the minimum proportion of observations that will fall within a specified number of standard deviations (k>1).

Define Dispersion in statistics.

The relative distribution or arrangement of individuals within a given amount of space.

What is the Empirical Rule?

In a bell-shaped distribution, about 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three standard deviations.

What is A priori Probability?

Probability that is known from a theoretical understanding of an experiment.

What is the Complement of an Event?

The probability that an event will not occur.

Define Conditional Probability.

The probability of one event occurring given that another event has occurred.

What is Sample Space?

A collection or a set of possible outcomes of a random experiment.

What is Subjective Probability?

Probability assessment based on experience, intuitive judgment, or expertise.

What are Exhaustive Events?

Events in a probability distribution where at least one of them must occur.

Define a Discrete Probability Distribution.

A probability distribution with a finite number of possible outcomes.

What does the Law of Large Numbers state?

The larger the sample size, the closer the sample mean will be to the population mean.

What are the Characteristics of a Probability Distribution?

1. Probability of each outcome is between 0 and 1; 2. Outcomes are mutually exclusive; 3. The list is exhaustive; 4. Sum of probabilities equals 1.

What are the assumptions of the Binomial Distribution?

1. n identical trials; 2. Two possible outcomes (success or failure); 3. Trials are independent; 4. Constant p and q.

Describe the Poisson Distribution.

A discrete distribution that describes rare events, where occurrences are independent over a continuum with expected occurrences constant.

What characterizes a Normal Probability Distribution?

Bell-shaped, symmetrical about the mean, asymptotic to the X-axis, and with mean, median, and mode being equal.

What is the Central Limit Theorem?

Under appropriate conditions, the distribution of the sample mean approaches a normal distribution as sample size increases.

What is the Null Hypothesis?

A statement assumed to be true until evidence indicates otherwise.

What is the Alternative Hypothesis?

The claim that is considered true if the null hypothesis is rejected.

Define p-value in hypothesis testing.

The lowest level of significance for which the null hypothesis can be rejected.

What is a Type I Error?

Rejecting the null hypothesis when it is actually true.

What is a Type II Error?

Not rejecting the null hypothesis when it is actually false.

What is Linear Regression?

A method to express the relationship between variables to estimate one based on the other.

What is Correlation Analysis?

The study of the relationship between two variables.

What is the formula for Standard Deviation?

Standard Deviation = Sqrt. of Variance.

Define the Binomial Formula.

P(X = x) = n!/(n-x)!x!·p^x(1 − p)^(n-x).

What is the Poisson formula?

P(X = x) = e^(-μ) * μ^x / x!, where μ is the long-run average.

What is the Standard Error for Sample Proportion?

SEP = sqrt(p(1-p)/n), where p is the sample proportion and n is the sample size.

What is meant by 'Confidence Level'?

The probability that a parameter will fall within a specified range.

What are the critical Z-values for 90%, 95%, and 99% confidence levels?

90% = 1.645, 95% = 1.96, 99% = 2.58.