All Flashcards
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 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.
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.