Sampling Distributions - Means

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 population's distribution.

Front

Define the mean of a sampling distribution.

Back

The mean of a sampling distribution is equal to the mean of the population from which the samples are drawn.

Front

What is the standard error of the mean?

Back

The standard error of the mean (SEM) is the standard deviation of the sampling distribution of the sample mean, calculated as the population standard deviation divided by the square root of the sample size (SEM = σ/√n).

Front

How does sample size affect the standard error?

Back

As the sample size increases, the standard error decreases, leading to a more precise estimate of the population mean.

Front

What is the formula for calculating the z-score in a sampling distribution?

Back

The z-score is calculated using the formula: z = (X̄ - μ) / (σ/√n), where X̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Front

What does it mean if a sampling distribution is approximately normal?

Back

If a sampling distribution is approximately normal, it means that the distribution of sample means will form a bell-shaped curve, allowing for the use of normal probability calculations.

Front

What is the significance of a right-skewed distribution in sampling?

Back

A right-skewed distribution indicates that there are a larger number of lower values, which can affect the mean and standard deviation of the sample means.

Front

How do you interpret a p-value in the context of sampling distributions?

Back

A p-value indicates the probability of obtaining a sample mean at least as extreme as the observed mean, assuming the null hypothesis is true.

Front

What is the relationship between population distribution and sampling distribution?

Back

While the population distribution can be skewed or non-normal, the sampling distribution of the sample mean will tend to be normal if the sample size is large enough due to the Central Limit Theorem.