AP Stats Unit 6-Confidence Interval Procedures

What is the definition of each confidence interval procedure? What are their conditions?

One Sample Z-Interval for a population proportion

Estimating the proportion of of successes in a single population

Conditions of a One Sample Z-Interval for a population proportion

Independence:

Data collected using a random Sample

Sample Size n is ≥10% of N

\
Approximately Normal:

Large counts n(p̂ )≥ 10 and n(1-p̂ )≥10

What is the form of Confidence Intervals

CI= point estimate ± margin of error

What is the point estimate?

Value of random variable

Ex: p̂ or x̄

How do you find moE?

critical value(standard error of statistic)

2 sample Z interval for a difference in proportions

Estimating the difference in proportions

When is it appropriate to use a 2 sample Z interval for a difference in proportions?

When either:

2 random samples have been selected

subjects are randomly assigned to 2 random groups

Conditions of a Two Sample Z-Interval for a population proportion

Independence:

Data collected using TWO random Samples

Sample Size n is ≥10% of N for BOTH samples

\
Approximately Normal:

Large counts n(p̂ )≥ 10 and n(1-p̂ )≥10 for BOTH samples

How do you find the confidence interval for a difference in proportions?

(p1-p2)± z\*(standard error of statistic)

2 sample T interval for a difference in means

Estimating the difference in means

One Sample T-Interval for a population mean

Estimating the mean in a single population

Conditions of a One Sample Z-Interval for a population proportion

Independence:

Data collected using a random sample

Sample Size n is ≥10% of N

\
Normal Distribution:

n is greater than or equal to 30

If n < 30 data MUST be free from strong skewness or outliers

How do you find T\* using calculator?

Inverse t distribution

area: 1 - C% as a decimal…divide that value by 2

df: n-1

How do you find Z\* using calculator?

Inverse norm distribution

area (Central): C% as a decimal

mean: 0

SD: 1

paired t-test

sample comes from