Chapter 17: Sampling Distributions

Question 1

Parameter

Answer 1

A value that describes some characteristic of the population

Question 2

Statistic

Answer 2

A value that describes some characteristic of a sample (used to estimate a parameter)

Question 3

Sampling Distribution

Answer 3

The distribution of values for a statistic for all possible samples of a given size from a given population

Question 4

Sampling Variability

Answer 4

The value of a statistic varies in a repeated random sampling

Question 5

Unbiased Estimator

Answer 5

When estimating a parameter, an estimator is unbiased if, on average, the value of the estimator is equal to the population parameter

Question 6

Variation In Sample Means

Answer 6

When estimating a population parameter, an estimator exhibits variation that can be modeled using probability.

Question 7

Mean & Standard Deviation Of A Sample Proportion

Answer 7

μp̂ = p
σp̂ = squareroot([p{1-p}]/n)
Assuming sample size is less than 10% of the population size or if sampling with replacement

Question 8

Conditions Of Sampling A Proportion

Answer 8

1. Randomly selected
2. n≤10% of population size
3. np≥10 & n(1-p)≥10

Question 9

Mean & Standard Deviation Of Difference Of Proportions

Answer 9

μp̂1-p̂2 = p1-p2
σp̂1-p̂2 = squareroot({[p1{1-p1}]/n1}+{[p2{1-p2}]/n2})
Assuming n≤10% of pop.
Sampling distribution of p̂1-p̂2 will be approx. normal when:
1. n1p1≥10
2. n1(1-p1)≥10
3. n2p2≥10
4. n2(1-p2)≥10

Question 10

Mean & Standard Deviation Of A Sample Mean

Answer 10

μx̄ = μ
σx̄ = σ/squareroot(n)

Question 11

Conditions For Sample Means

Answer 11

1. Random sample
2. n≤10% of pop.
3. n≥30 by CLT

Question 12

Mean & Standard Deviation Of Differences Of Sample Means

Answer 12

μx̄1-x̄2 = μ1-μ2
σx̄1-x̄2 = squareroot([σ1^2/n1]+[σ2^2/n2])
Assuming n1 & n2≤10% of pop. & n1 & n2≥30

Question 13

Standard Deviation Of Sample Proportions Interpretation

Answer 13

“The sample proportion of [success context] typically varies by [σp̂] from the true proportion of [p].”

Question 14

Standard Deviation Of Sample Means Interpretation

Answer 14

“The sample mean amount of [x-context] typically varies by [σx̄] from the true mean of [μX].”