AP Statistics - Chapter 7

7.1

Population - total group being focus on

• Parameter - proportion of population

Sample - group out of population being evaluated

• Statistic - proportion of sample

A statistic is an unbiased estimator of a parameter if the sampling distribution mean is equal to the parameter

An increase in sample size decreases variability

7.2

Evaluating a Claim:

1. Assume it’s true

2. Created a simulated sampling distribution

3. Find the percent chance of getting observed result and evaluate

If a sample occurs that is less than 5% of the sampling distribution, then there is convincing evidence to disprove a claim, if it is greater than 5%, there is not convincing evidence

7.3

10% Condition (checks for independence): if a sample is less than or equal to 10% of a population, independence can be assumed

Large Counts Condition (checks for normality): if np≥10 and n(1-p)≥10, then the distribution is approximately normal

µ(p̂) = p

σ(p̂) = √((p(1-p))/n)

z = (p̂-µ(p̂))/(σ(p̂))

7.4

Two Sample Distributions (two samples being combined into one sampling distribution)

µ(p̂1-p̂2) = p1-p2

σ(p̂1-p̂2) = √((p1(1-p1))/n1+(p2(1-p2))/n2)

z = ((p̂1-p̂2)-µ(p̂1-p̂2))/(σ(p̂1-p̂2))

7.5

µ(x̄) = µ

σ(x̄) = σ/√(n)

z = (x̄-µ(x̄))/(σ(x̄))

If the shape of a population is approximately normal, then the shape of the sampling distribution is approximately normal.

7.6

Central Limit Theorem: a sampling distribution is approximately normal is n≥30

7.7

Two Sample Distributions (two samples being combined into one sampling distribution)

µ(x̄1-x̄2) = µ(x̄1) - µ(x̄2) = µ(1) - µ(2)

σ(x̄1-x̄2) = √((σ1^2)/n1 + (σ2^2)/n2)

z = ((x̄1-x̄2)-µ(x̄1-x̄2))/(σ(x̄1-x̄2))