AP Statistics Chapter 8 Review

What is a point estimator?

A statistic that provides an estimate of a population parameter.

What is a point estimate?

The value of a statistic

What variables are used if it is categorical?

p hat and p

What variables are used if it’s quantitative?

x bar and mew

What happens when you have a higher confidence interval what increases?

The length of the confidence level increases.

What is a confidence interval?

Interval of possible values for a parameter based on sample data and it takes the form of:

Point Estimate +- M.E.

What is confidence level?

Gives the overall success rate of the method to calculate the confidence interval.

How do you interpret confidence interval?

We are ____% confident that the interval from ____ to ___ captures the [parameter in context]

EX:

We are 9% confident that the interval from 0.4 to 0.8 captures the true proportion of people who get to church on time.

How do you find Margin of Error given two intervals?

Find the difference of the two intervals and divide by two.

It is recommended that high school students get 8 hours of sleep each night. Based on this survey, the students claim that students at this high school are not getting the recommended amount of sleep. Use the confidence interval (5.39, 7.81) to evaluate this claim.

We fail to reject their claim. Look at the interval, 8 hours is not contained within that interval meaning students on average, tend to get less than 8 hours of sleep.

What do confidence levels tell us?

How likely it is that the method we are using will produce an interval that captures the population parameter if we use it many times.

Why do we tend to calculate only a single confidence interval for a given situation?

Because we only take one sample.

REMEMBER: Confidence level IS NOT a __________

probability

What does Margin of Error Account for?

Sampling variability due only to random selection. If you have bias, you shouldn’t have a confidence.

How do you interpret a confidence level?

If we used the same procedure of _____ many times, [confidence level] of the intervals would contain the true population parameter.

How would the margin of error change if we decreased the confidence interval? What if we increased it?

The margin of error would decrease; the m.e. would increase

What is the Large Counts Condition?

When np and n(1-p)>10

*p hat

Instead of using 2 to calculate 95% of the data, use….

1.96

How do you find the critical value (z*) for a random confidence level like 96%?

invNorm(A: C%/2 +.50 O: 1 U: 0

When finding the confidence interval via the calculator, make sure to additionally find the ______

Critical value

What is the four step process for finding confidence intervals?

1. State - What parameter do you want to estimate, and at what confidence intervals

2. Plan - Identify the appropriate inference method (CHECK CONDITIONS)

3. Do: If the conditions are met, perform calculations

4. Conclude - Interpret your interval in the context of the problem.

What formula do we use to determine the sample size GIVEN: Confidence Interval & Margin of Error?

ME> z*sigma/sqrt(n)

MAKE SURE YOU ROUND (CATEGORICAL DATA!!!)

When you determine the sampling distribution for ^p1-^p2, you MUST….

check the conditions FOR BOTH SAMPLES

When do we use standard error?

When the true population standard deviation or whatever is unknown.

What does 1 prop z-interval find?

The upper and lower boundary for 1 true proportion

What does 2 prop z-interval find?

The upper and lower boundary for 2 different populations

PLEASE NOTE AND STAR!

If you are trying to find the sample size given the ME and confidence interval BUT not the success/fail rate, USE ____

USE 0.5!!!!!!!!

What is the formula when you are trying to find N?

z*sqrt(p-hat*(1-p^)/n < ME

YOU USUALLY HAVE TO ASSUME THAT P HAT IS 0.5 if you’re given a specific Margin of Error.

When being asked to construct and interpret a C% interval for two populations, instead of doing the algebra, just do _____

2 prop z interval

How do we decrease margin of error without changing the confidence level?

Increase the sample size

How do you find p-hat given a confidence interval?

Add up the lower boundary and upper boundary and divide by two!

What does Margin of Error account for?

ONLY sampling variability!!!!! It does NOT account for any sort of biases.