Confidence Interval
Definition
A confidence interval is a range of values that is likely to contain the true value of a population parameter. It provides an estimate along with a level of confidence about how accurate the estimate is.
Analogy
Imagine you are trying to hit a target with darts. The bullseye represents the true value of the population parameter. The confidence interval is like a ring around the bullseye, showing you where your dart is likely to land.
Related terms
Margin of Error: The margin of error is the maximum amount by which an estimate might differ from the true value. It indicates the precision or accuracy of the estimate.
Sample Size: Sample size refers to the number of individuals or observations included in a study or survey. A larger sample size generally leads to narrower confidence intervals and more precise estimates.
Confidence Level: The confidence level represents how confident we are that our calculated interval contains the true population parameter. Commonly used levels include 90%, 95%, and 99%.
"Confidence Interval" appears in:
Study guides (12)
AP Statistics - 6.2 Constructing a Confidence Interval for a Population Proportion
AP Statistics - 6.3 Justifying a Claim Based on a Confidence Interval for a Population Proportion
AP Statistics - 6.9 Justifying a Claim Based on a Confidence Interval for a Difference of Population Proportions
AP Statistics - 6.10 Setting Up a Test for the Difference of Two Population Proportions
AP Statistics - 6.11 Carrying Out a Test for the Difference of Two Population Proportions
AP Statistics - 7.2 Constructing a Confidence Interval for a Population Mean
AP Statistics - 7.3 Justifying a Claim About a Population Mean Based on a Confidence Interval
AP Statistics - 7.4 Setting Up a Test for a Population Mean
AP Statistics - 7.6 Confidence Intervals for the Difference of Two Means
AP Statistics - 7.7 Justifying a Claim About the Difference of Two Means Based on a Confidence Interval
AP Statistics - 7.10 Skills Focus: Selecting, Implementing, and Communicating Inference Procedures
AP Statistics - 9.3 Justifying a Claim About the Slope of a Regression Model Based on a Confidence Interval
Additional resources (5)
Practice Questions (20+)
- Which of the following best describes a confidence interval?
- Which of the following factors affects the width of a confidence interval?
- To construct a confidence interval, we add and subtract a multiple of the SEM from the:
- Which statistic is used to calculate the margin of error for a confidence interval?
- What is the recommended approach for calculating a confidence interval for the population slope?
- What does the margin of error represent in a confidence interval?
- Which is a condition for constructing a confidence interval?
- Which of the following could narrow a confidence interval?
- What does the confidence level reflect in a confidence interval?
- What does the confidence interval (1.35, 2.7) suggest about the correlation?
- How can we justify a claim about a linear regression model using a confidence interval?
- If the confidence interval for the slope of a regression model is (-0.5, 1.2), what can we conclude?
- How does the width of a confidence interval change as the standard error of the slope decreases?
- If the confidence interval for the slope of a regression model is (-2.3, -0.7), what can we conclude?
- As sample size increases what happens to the width of the confidence interval for the slope of a regression model?
- If a confidence interval for the slope of a linear regression model is (-1.8, -0.2), what does this imply about the correlation between the variables?
- What is the purpose for justifying a claim using a confidence interval?
- If the confidence interval for the slope of a regression model is (-0.3, 0.3), what can we conclude?
- What does it mean if the resulting confidence interval for the difference in population proportions contains 0?
- What is the "margin of error" in a confidence interval for the difference of two population proportions based on?
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