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Questions and Answers
What is the confidence interval for proportions?
What is the confidence interval for proportions?
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 known?
Confidence Interval for Means when Sigma is Known
What is the confidence interval for means when Sigma is unknown?
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?
What does the margin of error represent?
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When the margin of error increases, what happens to the interval?
When the margin of error increases, what happens to the interval?
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When the margin of error decreases, what happens to the interval?
When the margin of error decreases, what happens to the interval?
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If confidence level increases, then critical value ______, ME ________, and interval gets __________.
If confidence level increases, then critical value ______, ME ________, and interval gets __________.
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If standard deviation increases, then ME ________ and interval gets ________.
If standard deviation increases, then ME ________ and interval gets ________.
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If sample size increases, then ME ________ and interval gets __________.
If sample size increases, then ME ________ and interval gets __________.
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For proportions, what value do you use?
For proportions, what value do you use?
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Use z* for means if ____ is known.
Use z* for means if ____ is known.
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Use t* for means if _____ is known.
Use t* for means if _____ is known.
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What does standard error mean?
What does standard error mean?
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What is standard error for proportions?
What is standard error for proportions?
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What is standard error for means?
What is standard error for means?
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Do confidence intervals deal with probability?
Do confidence intervals deal with probability?
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How do you interpret confidence levels?
How do you interpret confidence levels?
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When the margin of error increases, the interval gets ______.
When the margin of error increases, the interval gets ______.
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When the margin of error decreases, the interval gets _______.
When the margin of error decreases, the interval gets _______.
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What is a point estimator?
What is a point estimator?
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As sample size increases, the interval ________.
As sample size increases, the interval ________.
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As confidence level increases, the critical value ________.
As confidence level increases, the critical value ________.
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Confidence level isn't a __________, but it is a ___________ ______.
Confidence level isn't a __________, but it is a ___________ ______.
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The margin of error decreases when the confidence level ________.
The margin of error decreases when the confidence level ________.
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The margin of error decreases when the sample size ___________.
The margin of error decreases when the sample size ___________.
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If p hat is not mentioned when trying to find a sample size, use _______.
If p hat is not mentioned when trying to find a sample size, use _______.
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What does margin of error equal for proportions?
What does margin of error equal for proportions?
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What does margin of error equal for means?
What does margin of error equal for means?
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Does a t or z have more variability? Why?
Does a t or z have more variability? Why?
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How do you find degrees of freedom?
How do you find degrees of freedom?
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A t distribution with a bigger sample size has _______ variability in the tails.
A t distribution with a bigger sample size has _______ variability in the tails.
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Procedures that are not strongly affected when a condition for using them is violated are called ______.
Procedures that are not strongly affected when a condition for using them is violated are called ______.
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Robust procedures are...
Robust procedures are...
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If outliers are present in the sample, then the population may not be __________.
If outliers are present in the sample, then the population may not be __________.
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Are t procedures robust against outliers?
Are t procedures robust against outliers?
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Are x bar and Sx resistant to outliers?
Are x bar and Sx resistant to outliers?
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You can safely use the one-sample t procedures when _______ unless an ___________ or ______________ is present.
You can safely use the one-sample t procedures when _______ unless an ___________ or ______________ is present.
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What should be done with sample sizes less than 15?
What should be done with sample sizes less than 15?
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What about sample size at least 15?
What about sample size at least 15?
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What about large samples?
What about large samples?
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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.
Studying That Suits You
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Description
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.
