AP Statistics Chapter 8 Test Review
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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?

<p>the right side of the interval</p> Signup and view all the answers

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

<p>gets wider</p> Signup and view all the answers

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

<p>gets narrower</p> Signup and view all the answers

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

<p>increases, increases, wider</p> Signup and view all the answers

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

<p>increases, wider</p> Signup and view all the answers

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

<p>decreases, narrower</p> Signup and view all the answers

For proportions, what value do you use?

<p>z*</p> Signup and view all the answers

Use z* for means if ____ is known.

<p>sigma</p> Signup and view all the answers

Use t* for means if _____ is known.

<p>Sx</p> Signup and view all the answers

What does standard error mean?

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

What is standard error for proportions?

Signup and view all the answers

What is standard error for means?

Signup and view all the answers

Do confidence intervals deal with probability?

<p>False</p> Signup and view all the answers

How do you interpret confidence levels?

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

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

<p>wider</p> Signup and view all the answers

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

<p>narrower</p> Signup and view all the answers

What is a point estimator?

<p>a statistic that provides an estimate of a population parameter</p> Signup and view all the answers

As sample size increases, the interval ________.

<p>decreases</p> Signup and view all the answers

As confidence level increases, the critical value ________.

<p>increases</p> Signup and view all the answers

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

<p>probability, capture rate</p> Signup and view all the answers

The margin of error decreases when the confidence level ________.

<p>decreases</p> Signup and view all the answers

The margin of error decreases when the sample size ___________.

<p>increases</p> Signup and view all the answers

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

<p>0.5</p> 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?

<p>or t*</p> Signup and view all the answers

Does a t or z have more variability? Why?

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

How do you find degrees of freedom?

<p>n-1</p> Signup and view all the answers

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

<p>less</p> Signup and view all the answers

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

<p>robust</p> Signup and view all the answers

Robust procedures are...

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

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

<p>normal</p> Signup and view all the answers

Are t procedures robust against outliers?

<p>False</p> Signup and view all the answers

Are x bar and Sx resistant to outliers?

<p>False</p> Signup and view all the answers

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

<p>n ≥ 15, outlier, skewness</p> Signup and view all the answers

What should be done with sample sizes less than 15?

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

What about sample size at least 15?

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

What about large samples?

<p>t procedures can be used even for clearly skewed distributions when n ≥ 30</p> 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.

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