Sampling Distributions and Proportions

Front

What is a sampling distribution?

Back

A sampling distribution is the probability distribution of a statistic (like the sample mean) obtained from a large number of samples drawn from a specific population.

Front

What is the Central Limit Theorem?

Back

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normally distributed if the sample size is sufficiently large, regardless of the shape of the population distribution.

Front

What does it mean if a distribution is right-skewed?

Back

A right-skewed distribution has a longer tail on the right side, meaning that most values are concentrated on the left with fewer larger values.

Front

What is the symbol for population standard deviation?

Back

The symbol for population standard deviation is σ (sigma).

Front

What is a parameter in statistics?

Back

A parameter is a numerical value that summarizes a characteristic of a population, such as the population mean or population proportion.

Front

What is a statistic in statistics?

Back

A statistic is a numerical value that summarizes a characteristic of a sample, such as the sample mean or sample proportion.

Front

What happens to the shape of the sampling distribution as the sample size (n) increases?

Back

As the sample size increases, the shape of the sampling distribution becomes narrower and more normal.

Front

What is the formula for the standard error of the mean?

Back

The standard error of the mean (SEM) is calculated as SEM = σ / √n, where σ is the population standard deviation and n is the sample size.

Front

What does P(x̄ ≥ 10) represent?

Back

P(x̄ ≥ 10) represents the probability that the sample mean is at least 10.

Front

What is the difference between a sample and a population?

Back

A population includes all members of a specified group, while a sample is a subset of the population used to make inferences about the population.