Chapter 8: Sampling Distributions

Question 1

parameter

Answer 1

numerical summary of the population

Question 2

statistic

Answer 2

numerical summary of a sample

Question 3

sampling distribution

Answer 3

probability distribution for all possible values of the statistic computed from the sample size n

Question 4

sampling distribution of the mean x̄

Answer 4

probability distribution of all possible values of the mean x̄ of a sample with size n

Question 5

What is the mean of the sampling distribution of x̄?

Answer 5

μ_x̄ = μ_x

Question 6

What is the standard deviation of the sampling distribution of x̄?

Answer 6

σ_x̄ = σ_x/sqrt(n)

Question 7

central limit theorem

Answer 7

regardless of the shape of the original population, the sampling distribution of x̄ becomes approximately normal as the sample size n increases

Question 8

What does n have to be for the central limit theorem to be satisfied?

Answer 8

n ≥ 30

Question 9

sample proportion

Answer 9

proportion of individuals from the sample that has a certain characteristic

Question 10

What is the formula for sample proportion?

Answer 10

p̂ = x/n

Question 11

sampling distribution of p̂

Answer 11

probability distribution for all possible values of p̂ from the sample size n

Question 12

What is the mean of the sampling distribution of p̂?

Answer 12

μ_p̂ = p

Question 13

What is the standard deviation of the sampling distribution of p̂?

Answer 13

σ_p̂ = sqrt(pq/n)

Question 14

What are the conditions for the sampling distribution of p̂ to be normal?

Answer 14

npq ≥ 10 and 20n ≤ N