Unit Five: Sampling Distributions- essential knowledge

What does variation in statistics for samples taken from the same population indicate?

Variation can be either random or not random, depending on the sample.

What is a continuous random variable?

It is a variable that can take any value within a specified domain, with each interval having an associated probability.

What does a normal distribution describe?

It describes populations using a bell-shaped curve, where the distribution of a continuous random variable is symmetric and centered around the mean.

What does the area under a normal curve represent?

The area represents the probability that a particular value lies within a specific interval.

How can the boundaries of an interval in a normal distribution be determined?

Boundaries can be found using z-scores, technology (like a calculator), a standard normal table, or computer-generated output.

Why are normal distributions useful for approximating other distributions?

Because they are symmetrical and bell-shaped, making them applicable for distributions with similar characteristics.

What is a sampling distribution of a statistic?

It is the distribution of values for a statistic across all possible samples of a given size from a population.

What does the Central Limit Theorem (CLT) state?

The CLT states that when the sample size is large enough, the sampling distribution of the sample mean is approximately normally distributed.

What conditions are necessary for the Central Limit Theorem to hold?

The sample values must be independent, and the sample size should be sufficiently large.

What is a randomization distribution?

It is a collection of statistics generated by simulation, assuming known parameter values, often by randomly reassigning response values to treatment groups.

How can the sampling distribution of a statistic be simulated?

By generating repeated random samples from a population.

What does it mean if an estimator is unbiased?

An unbiased estimator has a long-term average value equal to the population parameter.

Why does an estimator exhibit variability?

Because the sample statistic varies due to chance, which can be modeled using probability.

What is a sample statistic?

It is a point estimator used to estimate the corresponding population parameter.

How does sampling without replacement affect the standard deviation of the sample proportion?

The standard deviation is slightly smaller than expected if the sample size is less than 10% of the population, making the difference negligible.

Under what conditions will the sampling distribution of a sample proportion be approximately normal?

When both np ≥ 10 and n(1 - p) ≥ 10.

How should probabilities and parameters for a sampling distribution of a sample proportion be interpreted?

They should be interpreted within the context of a specific population and in appropriate units.

How does sampling without replacement affect the standard deviation of the difference in sample proportions?

The standard deviation is slightly smaller than expected if the sample sizes are less than 10% of the population sizes, making the difference negligible.

Under what conditions will the sampling distribution of the difference in sample proportions be approximately normal?

When n₁p₁ ≥ 10, n₁(1 - p₁) ≥ 10, n₂p₂ ≥ 10, and n₂(1 - p₂) ≥ 10.

How should parameters for a sampling distribution of a difference in proportions be interpreted?

They should be interpreted within the context of specific populations and in appropriate units.

How does sampling without replacement affect the standard deviation of the sample mean?

The standard deviation is slightly smaller than expected if the sample size is less than 10% of the population, making the difference negligible.

Under what conditions can the sampling distribution of the sample mean be modeled with a normal distribution?

If the population distribution is normally distributed or if the sample size is large enough (typically n ≥ 30).

How should probabilities and parameters for a sampling distribution of a sample mean be interpreted?

They should be interpreted within the context of a specific population and in appropriate units.

How does sampling without replacement affect the standard deviation of the difference in sample means?

The standard deviation is slightly smaller than expected if the sample sizes are less than 10% of the population sizes, making the difference negligible.

Under what conditions can the sampling distribution of the difference in sample means be modeled with a normal distribution?

If both population distributions are normally distributed or if the sample sizes are both greater than or equal to 30.

How should parameters for a sampling distribution of a difference in sample means be interpreted?

They should be interpreted within the context of specific populations and in appropriate units.