Sampling Distributions Assessment

Front

What is a sampling distribution?

Back

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

Front

What does it mean for an estimator to be unbiased?

Back

An estimator is unbiased if its expected value equals the true value of the parameter being estimated.

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, regardless of the population's distribution, as long as the sample size is sufficiently large (usually n ≥ 30).

Front

What is the formula for the mean of a sampling distribution of sample proportions?

Back

The mean of the sampling distribution of sample proportions is equal to the population proportion (p).

Front

What is the standard error of a sample proportion?

Back

The standard error of a sample proportion is calculated using the formula: SE = sqrt[(p(1-p)/n)], where p is the sample proportion and n is the sample size.

Front

What is the significance of np and nq in determining the shape of a sampling distribution?

Back

For a sampling distribution of proportions to be approximately normal, both np and nq must be greater than or equal to 10, where p is the population proportion and q = 1 - p.

Front

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

Back

A sampling distribution is approximately normal if it follows a bell-shaped curve, which allows for the application of normal probability methods.

Front

How does sample size affect the shape of the sampling distribution?

Back

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

Front

What is the relationship between the sample size and the standard error?

Back

The standard error decreases as the sample size increases, indicating that larger samples provide more precise estimates of the population parameter.

Front

What is a biased estimator?

Back

A biased estimator is one where the expected value does not equal the true value of the parameter being estimated.