Unit 7, "Sampling Distributions,"

Term: Parameter

A number that describes some characteristic of a population

Term: Statistic

Definition: A number that estimates the value of a parameter using a sample from the population

Question: What is a sampling distribution?

Answer: The distribution of values taken by a statistic in all possible samples of the same size from the same population

Question: What is the mean of the sampling distribution of a sample proportion?

Answer: μp̂ = p (where p is the population proportion)

Question: What is the standard deviation of the sampling distribution of a sample proportion?

Answer: σp̂ = √((p(1-p))/n) (where n is the sample size)

Question: What conditions must be met to use the formula for σp̂?

Answer: 10% condition: n ≤ (.10)N (sample size is no more than 10% of the population size)

Term: Central Limit Theorem (CLT)

Definition: For a large sample size, the sampling distribution of the sample mean is approximately Normal, regardless of the shape of the population distribution

Question: What is the mean of the sampling distribution of a sample mean?

Answer: μx̄ = μ (where μ is the population mean)

Question: What is the standard deviation of the sampling distribution of a sample mean?

Answer: σx̄ = σ/√n (where σ is the population standard deviation and n is the sample size)

Question: When can you use a Normal distribution to calculate probabilities involving sample means?

Answer: When the population distribution is Normal or the sample size is large (n ≥ 30)

Question: What is the purpose of a sampling distribution?

Answer: To make inferences about a population based on a sample

Question: What is a point estimate?

Answer: Single best guess for the value of a population parameter

Question: What is the effect of increasing the sample size on the variability of the sampling distribution?

Answer: Increasing the sample size decreases the variability

Question: What is the difference between a statistic and a parameter?

Answer: A parameter describes the population, while a statistic describes a sample

Question: What is the 10% condition and why is it important?

Answer: When sampling without replacement, the sample size n should be less than 10% of the population size N (n ≤ 0.10N) to use the standard deviation formula for sample proportions