AP Stats Unit 6 quiz one review

Confidence Interval

Range of values that is plausible for the true population parameter. Calculated by sample data!

Formula = point estimate ± margin of error

Confidence Level (C%)

How convinced we are that this interval captures the true parameter value. C is the area between 2 critical values (z*). Repeating a process = C% confident in true parameter being between confidence intervals.

Critical values (z*)

The boundaries of the confidence interval.

Formula: InvNorm( (100-C%)/200, 0, 1) = z*

There is no negatives for critical values, so make them all positive!

Interpreting Confidence Interval

“We are C% confident that the interval from ___ to ___ captures the true proportion of [context]”

Interpreting Confidence Levels

“If we take many sample sizes from this population, about __% of them will result in an interval that captures the actual parameter value.”

Conditions for Confidence Intervals

Random, Independent, and Normal

Random Condition

Randomly Selected (sampling) or Randomly Assigned (experiment)

Independent Condition

10% condition: n > 0.1N

No need to look/confirm this in experiments

Normal Condition

Large Counts Condition: np̂ > 10 and n(1-p̂) > 0.1 so the sampling distribution is approximately normal.

Standard Error

The standard deviations of our sampling distribution using p̂, not p. Shows how close p̂ will be to p in repeated SRS.

Formula: SEp̂ = { [ (p̂)(1-p̂ ) ] / n }

One Prop. Z-Int. (A)

Test for confidence intervals and confidence levels.