AP Stats Unit 6 (6.1-6.9)

confidence interval

point estimate ± margin of error

point estimate

A+B/2

margin of error

B-A/2

interpret confidence INTERVAL

we are [C.L] confident that the interval from [A] to [B] captures the [true parameter in context]

interpret confidence LEVEL

if we take many samples and construct an interval for each, about [C.L]% of them will capture the true [parameter in context]

what does margin of error account for?

sampling variability

if confidence level increases, margin of error…

increases

what happens to the interval when you INCREASE the MOE?

widens/gets larger

if sample size increases, MOE…

decreases

what happens to the interval when you DECREASE the MOE?

narrows/gets smaller

what does MOE NOT account for?

bias

what 3 conditions must be checked?

randomness, independence/10%, large counts

why is random condition important?

to generalize data to population

why is 10%/independent condition important?

to use standard error of p-hat

why is LCC important?

to show sampling distribution is approximately Normal

general formula for confidence interval of p

point estimate ± MOE

specific formula for p

what are the 4 C’s

choose, check, calculate, conclude

what is needed in the choose step

procedure, define parameter, confidence level

what should you avoid in the calculate step

symbols

formula for MOE when choosing sample size

what is the conservative estimate

p-hat=0.5

when do we use the conservative estimate

when sample has not been taken and p-hat is unknown

what must the sample size (n) be

a whole number

what is the procedure for a difference in proportions (p1-p2)

2 sample z interval for p1-p2

what is the procedure for a proportion

1 sample z interval for p

how many times do you need to check the conditions for a difference in proportions

twice

formula for a difference in proportions

what does a (+,+) confidence interval mean in terms of evaluating a claim

convincing evidence p1 is greater

what does a (-,-) confidence interval mean in terms of evaluating a claim

convincing evidence p2 is greater

what does a (-,+) confidence interval mean in terms of evaluating a claim

no convincing evidence of a difference

why does a (-,+) confidence interval mean no difference between proportions

because 0 is contained in the interval

what condition is skipped when there is no random sampling

10%/independence

what do you check in the Normal condition if the population distribution is not Normal

central limit theorem (CLT)

what if the CLT is still not met

quote or point from question that sample has no major skew or outliers

critical value for proportions

z*

critical value for means

t*

why do we use t* for means

because standard deviation is unknown

what do we use in Desmos for means instead of mean and standard deviation

degrees of freedom

degrees of freedom formula

df=n-1

as degrees of freedom increase, variance…

decreases

procedure for interval for means

1 sample t interval for μ

define μ

true mean of [parameter in context]

mean interval formula

procedure for difference in means

2 sample t interval for μ1-μ2

define μ1-μ2

true difference in means of [parameter in context]

if have independent random sample and/or RA

need check 10% condition

formula for difference of means

for which μ do you use their degree of freedom

the smaller one

what are the ONLY 2 things needed to be written if using Desmos for calculating difference of means

confidence interval and degrees of freedom used

procedure for mean difference

1 sample t interval for μD OR paired t interval for μD

define μD

true mean difference of [parameter in context]

how to determine sampling method used

read context of the problem

what do you treat differences as

1 sample of differences

formula for mean difference

x-bar ± t* sD/√n

what is compared in difference of means

independent, unrelated samples

what is compared in mean difference

paired data

what IS mean difference

average of differences of paired samples

how to change bounds of an interval

multiply by new given sample size and other value