Sampling Distributions

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 happens to the shape of the sampling distribution as the sample size increases?

Back

As the sample size increases, the shape of the sampling distribution approaches a normal distribution, regardless of the shape of the population distribution (Central Limit Theorem).

Front

What is the Central Limit Theorem?

Back

The Central Limit Theorem states that the distribution of the sample means will be approximately normally distributed if the sample size is sufficiently large (usually n ≥ 30), regardless of the population's distribution.

Front

What is the mean of the sampling distribution of sample means?

Back

The mean of the sampling distribution of sample means (μ_x-bar) is equal to the mean of the population (μ).

Front

What is the standard deviation of the sampling distribution of sample means?

Back

The standard deviation of the sampling distribution of sample means (σ_x-bar) is equal to the population standard deviation (σ) divided by the square root of the sample size (n): σ_x-bar = σ/√n.

Front

If a population is strongly right-skewed, what can be said about the sampling distribution for a sample size of 49?

Back

For a sample size of 49, the sampling distribution will be approximately normal due to the Central Limit Theorem.

Front

What is the probability of obtaining a sample proportion?

Back

The probability of obtaining a sample proportion can be calculated using the normal approximation to the binomial distribution when the sample size is large enough.

Front

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

Back

The z-score for a sample mean can be calculated using the formula: z = (x̄ - μ) / (σ/√n), where x̄ is the sample mean, μ is the population mean, and σ is the population standard deviation.

Front

What is the significance of a sample size of 30 in statistics?

Back

A sample size of 30 is often considered the minimum size for the Central Limit Theorem to hold, allowing the sampling distribution of the mean to be approximately normal.

Front

What does it mean if a sampling distribution is not normal?

Back

If a sampling distribution is not normal, it may indicate that the sample size is too small or that the population distribution is not suitable for normal approximation.