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.
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.
What is the general formula for a confidence interval?
Point Estimate ± (Critical Value * Standard Error)
What is the formula for the standard error of a sample proportion?
SE = sqrt[(p-hat * (1-p-hat))/n], where p-hat is the sample proportion and n is the sample size.
How is the width of a confidence interval related to the margin of error?
Width = 2 * MOE
How do you calculate sample proportion?
p-hat = number of successes in the sample / total number in the sample.
What is the formula for the margin of error (MOE) for a proportion?
MOE = z* * sqrt[(p-hat * (1-p-hat))/n], where z* is the critical value, p-hat is the sample proportion, and n is the sample size.
