AP Statistics Chapter 8 Test Review

Questions and Answers

What is the confidence interval for proportions?

Confidence Interval for Proportions

What is the confidence interval for means when Sigma is known?

Confidence Interval for Means when Sigma is Known

What is the confidence interval for means when Sigma is unknown?

Confidence Interval for Means when Sigma is Unknown

What does the margin of error represent?

the right side of the interval Signup and view all the answers

When the margin of error increases, what happens to the interval?

gets wider Signup and view all the answers

When the margin of error decreases, what happens to the interval?

gets narrower Signup and view all the answers

If confidence level increases, then critical value , ME , and interval gets ____.

increases, increases, wider Signup and view all the answers

If standard deviation increases, then ME and interval gets .

increases, wider Signup and view all the answers

If sample size increases, then ME and interval gets __.

decreases, narrower Signup and view all the answers

For proportions, what value do you use?

z* Signup and view all the answers

Use z* for means if ____ is known.

sigma Signup and view all the answers

Use t* for means if _____ is known.

Sx Signup and view all the answers

What does standard error mean?

in repeated sampling, the average distance from sample mean and population mean Signup and view all the answers

What is standard error for proportions?

Signup and view all the answers

What is standard error for means?

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Do confidence intervals deal with probability?

False Signup and view all the answers

How do you interpret confidence levels?

__% of all possible samples of the SAME size from the SAME population will result in an interval that captures the parameter Signup and view all the answers

When the margin of error increases, the interval gets ______.

wider Signup and view all the answers

When the margin of error decreases, the interval gets _______.

narrower Signup and view all the answers

What is a point estimator?

a statistic that provides an estimate of a population parameter Signup and view all the answers

As sample size increases, the interval ________.

decreases Signup and view all the answers

As confidence level increases, the critical value ________.

increases Signup and view all the answers

Confidence level isn't a ____, but it is a _ __.

probability, capture rate Signup and view all the answers

The margin of error decreases when the confidence level ________.

decreases Signup and view all the answers

The margin of error decreases when the sample size ___________.

increases Signup and view all the answers

If p hat is not mentioned when trying to find a sample size, use _______.

0.5 Signup and view all the answers

What does margin of error equal for proportions?

Signup and view all the answers

What does margin of error equal for means?

or t* Signup and view all the answers

Does a t or z have more variability? Why?

t has more variability because t comes from a sample so there is sampling variability Signup and view all the answers

How do you find degrees of freedom?

n-1 Signup and view all the answers

A t distribution with a bigger sample size has _______ variability in the tails.

less Signup and view all the answers

Procedures that are not strongly affected when a condition for using them is violated are called ______.

robust Signup and view all the answers

Robust procedures are...

procedures if the probability calculations involved in that procedure remain fairly accurate when a condition for using the procedure is violated Signup and view all the answers

If outliers are present in the sample, then the population may not be __________.

normal Signup and view all the answers

Are t procedures robust against outliers?

False Signup and view all the answers

Are x bar and Sx resistant to outliers?

False Signup and view all the answers

You can safely use the one-sample t procedures when _ unless an _ or __________ is present.

n ≥ 15, outlier, skewness Signup and view all the answers

What should be done with sample sizes less than 15?

use t procedures only if the data appears normal (no outliers or strong skewness) Signup and view all the answers

What about sample size at least 15?

t procedures can be used except in the presence of outliers or strong skewness Signup and view all the answers

What about large samples?

t procedures can be used even for clearly skewed distributions when n ≥ 30 Signup and view all the answers

Study Notes

Confidence Intervals for Proportions

Confidence Interval for Proportions measures the range of values in which the true population proportion is expected to fall.
Use z* as the critical value for constructing these intervals.

Confidence Intervals for Means

Confidence Interval for Means when Sigma is Known utilizes the known population standard deviation (sigma) for calculations.
Use z* as the critical value in this scenario.
Confidence Interval for Means when Sigma is Unknown uses the sample standard deviation (Sx) and requires t* as the critical value.

Margin of Error (ME)

Margin of Error represents the maximum expected difference between the true population value and the sample estimate.
ME increases result in a wider interval; decreasing ME results in a narrower interval.

Effects on Confidence Intervals

Higher confidence levels lead to larger critical values, thus increasing the ME and resulting in wider intervals.
Increasing standard deviation leads to increased ME and broader intervals.
Increasing sample size decreases ME, leading to narrower intervals.

Standard Error

Standard error quantifies the average distance from the sample mean to the population mean in repeated sampling.
Standard error for proportions and means depends on their respective formulas, which were not provided.

Interpretation of Confidence Levels

A confidence level indicates that a specific percentage of samples will create intervals capturing the parameter.

Point Estimators

Point estimator is a statistic used to estimate a population parameter, offering a single value rather than a range.

Critical Values and Robustness

Confidence level increases lead to higher critical values, while decreasing confidence leads to lower margin of error.
Robust procedures remain effective even when some conditions are violated, such as normality and the presence of outliers.

Outliers and Sample Size Considerations

T procedures are not robust against outliers and sample statistics like x̄ and Sx also lack resistance to outliers.
For samples n ≥ 15, t procedures are applicable unless outliers or strong skewness are present.
For n < 15, t procedures are valid only if the data is approximately normal with no outliers.

Large Samples

T procedures can be used for skewed distributions if the sample size is ≥ 30.

Degrees of Freedom

Degrees of freedom for t procedures is calculated as n - 1, influencing critical value determination and variability.

Variability in T Distributions

Increasing sample size reduces variability in the tails of the t distribution, making it resemble the normal distribution more closely.

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Prepare for your AP Statistics Chapter 8 exam with these flashcards. This review covers key concepts such as confidence intervals for proportions and means, as well as margin of error. Enhance your understanding and retention of statistical methods essential for mastering this chapter.

AP Statistics Chapter 8 Test Review

Questions and Answers

What is the confidence interval for proportions?

What is the confidence interval for means when Sigma is known?

What is the confidence interval for means when Sigma is unknown?

What does the margin of error represent?

When the margin of error increases, what happens to the interval?

When the margin of error decreases, what happens to the interval?

If confidence level increases, then critical value ______, ME ________, and interval gets __________.

If standard deviation increases, then ME ________ and interval gets ________.

If sample size increases, then ME ________ and interval gets __________.

For proportions, what value do you use?

Use z* for means if ____ is known.

Use t* for means if _____ is known.

What does standard error mean?

What is standard error for proportions?

What is standard error for means?

Do confidence intervals deal with probability?

How do you interpret confidence levels?

When the margin of error increases, the interval gets ______.

When the margin of error decreases, the interval gets _______.

What is a point estimator?

As sample size increases, the interval ________.

As confidence level increases, the critical value ________.

Confidence level isn't a __________, but it is a ___________ ______.

The margin of error decreases when the confidence level ________.

The margin of error decreases when the sample size ___________.

If p hat is not mentioned when trying to find a sample size, use _______.

What does margin of error equal for proportions?

What does margin of error equal for means?

Does a t or z have more variability? Why?

How do you find degrees of freedom?

A t distribution with a bigger sample size has _______ variability in the tails.

Procedures that are not strongly affected when a condition for using them is violated are called ______.

Robust procedures are...

If outliers are present in the sample, then the population may not be __________.

Are t procedures robust against outliers?

Are x bar and Sx resistant to outliers?

You can safely use the one-sample t procedures when _______ unless an ___________ or ______________ is present.

What should be done with sample sizes less than 15?

What about sample size at least 15?

What about large samples?

Study Notes

Confidence Intervals for Proportions

Confidence Intervals for Means

Margin of Error (ME)

Effects on Confidence Intervals

Standard Error

Interpretation of Confidence Levels

Point Estimators

Critical Values and Robustness

Outliers and Sample Size Considerations

Large Samples

Degrees of Freedom

Variability in T Distributions

Studying That Suits You

Description

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If confidence level increases, then critical value , ME , and interval gets ____.

If standard deviation increases, then ME and interval gets .

If sample size increases, then ME and interval gets __.

Confidence level isn't a ____, but it is a _ __.

You can safely use the one-sample t procedures when _ unless an _ or __________ is present.