Sampling Distributions #1

Front

What is a sampling distribution?

Back

A distribution showing the sample means of all samples of size n from a population.

Front

What is the mean of the sampling distribution of p-hat if the true proportion is 40%?

Back

0.4

Front

What is the Central Limit Theorem?

Back

The theorem states that the sampling distribution of the sample mean will be approximately normally distributed if the sample size is sufficiently large (n ≥ 30) or if the population is normally distributed.

Front

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

Back

Standard Error (SE) = σ / √n, where σ is the population standard deviation and n is the sample size.

Front

What is the significance of np and nq being greater than or equal to 10?

Back

It ensures that the sampling distribution of the sample proportion is approximately normal.

Front

What is the probability of a sample mean being less than a certain value?

Back

It can be calculated using the Z-score formula and the standard normal distribution.

Front

What does it mean if a sampling distribution is normal?

Back

It means that the distribution of sample means is symmetric and bell-shaped, allowing for the application of normal probability calculations.

Front

What is the relationship between sample size and the shape of the sampling distribution?

Back

As the sample size increases, the sampling distribution becomes more normal regardless of the population distribution.

Front

What is the standard deviation of the sampling distribution of the sample mean called?

Back

Standard Error of the Mean (SEM).

Front

How do you calculate the Z-score for a sample mean?

Back

Z = (X̄ - μ) / (σ / √n), where X̄ is the sample mean, μ is the population mean, and σ is the population standard deviation.