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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.
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.