AP Stat confidence interval

Confidence interval

Gives a set of plausible values for a parameter

Conditions for a confidence interval for proportion

Random, 10%, large counts

10%

n<0.10N

Large Counts

Both np̂ and n(1-p̂)≥ 10

Point Estimator p̂

A statistic that provides an estimate of a population parameter.

Sample proportion is an

unbiased estimator allowing for generalization of results to the population of interest

Confidence Level

Approximate percentage of confidence intervals that will capture the population parameter in repeated random samples with the sample size

Critical value

Multiplies that make the interval wide enough to have the stated capture rate

Standard Error

An estimate of the standard deviation of the sampling distribution p̂. Describes the sample proportion p̂ typically varies from the population proportion p in repeated random samples of size n.

Margin of error

An Estimate describing how far (at most) we expect the point estimate to vary from the population parameter.

How to determine the margin of error from a confidence interval

Subtract lowest from highest and then divide by 2

(0.713-0.544) /2=0.0795

How to determine the point estimate

Add the margin of error the lower end of the interval

0.544 + 0.0795=0.6335

Small sampling sizes have BLANK variability than larger sampling sizes

Greater

Increasing the sample size does what to the margin of error

Decreases it

What happens when the confidence level increases?

The margin of error increases which widens the confidence interval

The confidence interval becomes BLANK as the confidence level increases

Wider

The margin of error is larges at

p̂=0.50

Interpreting the confidence INTERVAL

We are C% confident that the interval from BLANK to BLANK captures the true proportion of…

Interpreting the confidence LEVEL

If we were to select many random samples of the same size from the same population and construc a C% confidence interval using each sample, about C% of the interval would capture the true proportion of…

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