AP STAT REVIEW: Inference

when the center of the sampling distribution of the statistic is equal to the population parameter

Random, 10% condition, large counts

the probability of obtaining a test statistic as extreme or more extreme than the observed test statistic when the null hypothesis is assumed to be true

distribution of responses for every individual of the population

Distribution of responses for a single sample

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

“We are C% confident that the confidence interval from to captures the [population parameter in context]

Suppose confidence interval is (A,B)

The point estimate is the average of A and B.

Suppose confidence interval is (A,B)

MoE = B - (Point Estimate)

#5: 1-PropZTest

#2: T-Test

n-1

t=(X BAR)-µ₀ / s/√n

t=(X BAR₁ - X BAR₂) / √s₁²/n₁ + s₂²/n₂ OR 2-samp T-Test

the probability a test will correctly reject the null hypothesis, given the alternate hypothesis is true

P(Type II error) = 1-P(Power)

z=(P HAT) - p₀ / √p₀(1-p₀)/n

#8: TInterval

(P HAT) ± z* √ (P HAT) (1-P HAT)/n

(X BAR) ± t* s/√n

A: 1-PropZInt

Decreases as n increases, increases as conf level increases

2-propZInt

So we can generalize to the population from which the sample was selected

so sampling without replacement is okay, and we can use the stated formula for standard deviation

so the sampling distribution is approximately normal

There is statistcial evidence to support the alternative hypothesis

there is not convincing statistical evidence to support the alternative hypothesis

2-sampTInt on calc

when the null hypothesis is true, but is rejected

when the alternate hypothesis is true, and the null is not rejected

does the scenario describe mean(s), proportion(s), counts, or slope?

Does the scenario describe one sample, 2 sample, or paired data

Does the scenario describe a test or confidence interval?

X₁+X₂/n₁+n₂

2-propZTest on calc

In repeated random sampling with the same sample size, approximately C% of confidence intervals created will capture the [population parameter in context].

a number that describes the population

number that describes the sample

b-β₀/SE(sub b) (df=n-2)

Random, 10%, large counts (all expected counts ≥5)

b±t* SE(sub b) (df=n-2)

x²=Σ (observed-expected)²/expected (df = #of groups -1)

expected count = (row total)(column total) / table total

X²=Σ (observed-expected)²/expected (df=number of groups-1)

X²=Σ (observed-expected)²/espected (df= (rows-1)(columns-1))

Our P-value [p=_] is LESS/GREATER than the significance level [ALPHA = _]. Therefore we REJECT/FAIL TO REJECT the null. We DO/NOT have statistical evidence for [alternate hypothesis].

If the P-value is low, reject that hoe. If the P-value is high, the null’s that guy.

The true distribution of [VARIABLE] is equally proportional as [ ] claims

The true distribution of [VARIABLE] is different than claimed.

There is no difference in the true distribution of [VAR] for [POP 1] and [POP 2].

There is a difference in the true distribution of [VAR] for [POP 1] and [POP 2].

Truly linear (no pattern in the residual plot), Independent (10%), Normal distribution of residuals at each X (histogram of residuals is normal-ish), Equal std. dev. of resid. for all X (no heteroskedacisity), random sample

n ≤ 1/10 N

np ≥ 10 and n(1-p) ≥ 10

n≥30