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What are the differences between interpreting a confidence interval and testing a claim using a confidence interval?
Interpreting: Explaining the meaning of the interval in context. | Testing: Evaluating whether a specific value falls within the interval to support or refute a claim.
What are the differences between a sample proportion and a population proportion?
Sample Proportion: Calculated from a sample. | Population Proportion: True proportion for the entire population (what we estimate).
What are the differences between a 90% and a 99% confidence interval (assuming the same data)?
90% CI: Narrower interval, lower confidence. | 99% CI: Wider interval, higher confidence.
What are the differences between using p-hat and p when checking the Large Counts condition?
p-hat: Used when no claim is given. | p: Used when testing a specific claim about the population proportion.
What are the differences between the confidence level and the confidence interval?
Confidence Level: The probability that the method will produce an interval that captures the true parameter. | Confidence Interval: The specific interval calculated from sample data.
Explain how sample size affects the width of a confidence interval.
As sample size increases, the width of the confidence interval decreases (inverse relationship).
Explain how confidence level affects the width of a confidence interval.
As confidence level increases, the width of the confidence interval increases (direct relationship).
How can a confidence interval be used to test a claim?
If the claimed proportion falls inside the interval, it's plausible. If it falls outside, it's less likely to be true.
Explain the importance of context when interpreting a confidence interval.
Always relate the interval back to the original problem. What are you estimating? This provides meaning to the numerical range.
Why is it important to check conditions before constructing a confidence interval?
Checking conditions (Random, Independent, Large Counts) ensures the validity of the confidence interval and the reliability of the conclusions drawn.
What is a confidence interval?
A range of values, calculated from sample data, likely to contain the true population parameter.
What is a population proportion?
The true percentage of a population that has a certain characteristic.
What is the confidence level?
The probability that the interval contains the true population proportion (e.g., 95%).
What is the margin of error?
The distance from the point estimate to the bounds of the confidence interval.
Define 'point estimate'.
A single value estimate of a population parameter based on sample data.