Stats Part 1

Question 1

What is the difference between descriptive and inferential statistics?

Answer 1

Descriptive summarizes data; inferential draws conclusions about populations from samples.

Question 2

What is a parameter in statistics?

Answer 2

A value that describes a characteristic of a population.

Question 3

What is a statistic in statistics?

Answer 3

A value calculated from a sample to estimate a population parameter.

Question 4

What is a population?

Answer 4

The complete group of individuals or items you want to study.

Question 5

What is a sample?

Answer 5

A subset of a population used for analysis.

Question 6

What is probability?

Answer 6

A measure of the likelihood of an event occurring.

Question 7

What are the three main interpretations of probability?

Answer 7

Classical, frequentist, and subjective.

Question 8

What is a random experiment?

Answer 8

A process that leads to one of several possible outcomes.

Question 9

What is a sample space?

Answer 9

The set of all possible outcomes of an experiment.

Question 10

What is a random variable?

Answer 10

A numerical quantity whose value depends on the outcome of a random experiment.

Question 11

What is the addition rule of probability?

Answer 11

P(A or B) = P(A) + P(B) − P(A and B)

Question 12

What is the multiplication rule of probability?

Answer 12

P(A and B) = P(A) × P(B|A)

Question 13

What is conditional probability?

Answer 13

P(A|B) is the probability of A given that B has occurred.

Question 14

What does it mean for two events to be independent?

Answer 14

The occurrence of one does not affect the probability of the other.

Question 15

What does it mean for two events to be mutually exclusive?

Answer 15

They cannot happen at the same time.

Question 16

What is Bayes’ Theorem?

Answer 16

A formula to update probabilities based on new evidence: P(A|B) = P(B|A)P(A)/P(B)

Question 17

What is a prior probability?

Answer 17

The initial estimate of a probability before seeing new data.

Question 18

What is a posterior probability?

Answer 18

The updated probability after taking new data into account.

Question 19

What is a likelihood in Bayes’ Theorem?

Answer 19

The probability of observing the data given a particular hypothesis.

Question 20

What is a probability distribution?

Answer 20

A function that describes the likelihood of different outcomes for a random variable.

Question 21

What is a discrete probability distribution?

Answer 21

A distribution for a variable that takes distinct, separate values.

Question 22

What is a continuous probability distribution?

Answer 22

A distribution for a variable that can take any value in a range.

Question 23

What is the binomial distribution used for?

Answer 23

Modeling the number of successes in a fixed number of independent trials.

Question 24

What is the normal distribution?

Answer 24

A bell-shaped, symmetric distribution defined by its mean and standard deviation.

Question 25

What is the Central Limit Theorem?

Answer 25

It states that the sampling distribution of the sample mean approaches normality as sample size increases.

Question 26

Why is the Central Limit Theorem important?

Answer 26

It allows us to make inferences about the population mean using normal methods.

Question 27

What is a sampling distribution?

Answer 27

The distribution of a statistic (like the mean) over many random samples.

Question 28

How does sample size affect the sampling distribution?

Answer 28

Larger samples lead to distributions closer to normal and with smaller spread.

Question 29

What is the law of large numbers?

Answer 29

As sample size grows, the sample mean approaches the population mean.