Confidence Interval Flashcards
What is a Binomial Distribution?
A discrete RV from fixed, independent Bernoulli trials. X ~ B(n, p); mean: μ = np, std dev: σ = √(np(1–p)).
What is a Confidence Interval (CI)?
An interval estimate for a population parameter based on confidence level, sample size, and known or estimated standard deviation.
What does Confidence Level (CL) represent?
The percentage of intervals expected to contain the true population parameter (e.g., 90% CL means 90 out of 100 contain the true value).
What are Degrees of Freedom (df)?
The number of values in a sample that are free to vary; typically n – 1.
What is the Error Bound for a Population Mean (EBM)?
The margin of error; depends on confidence level, sample size, and standard deviation.
What is Inferential Statistics?
Infers population parameters from sample statistics (e.g., estimating 4% defective from a sample).
What is a Normal Distribution?
A continuous RV X ~ N(μ, σ); if μ = 0 and σ = 1, it is the standard normal distribution.
What is a Parameter in statistics?
A numerical characteristic of a population, like population mean or proportion.
What is a Point Estimate?
A single number from a sample used to estimate a population parameter.
What is Standard Deviation?
A measure of spread around the mean; sample: s, population: σ.
What is Student’s t-Distribution?
Used when population σ is unknown; based on df, more spread out than the normal distribution.
How is a Confidence Interval for a mean with known σ calculated?
CI = point estimate ± EBM; EBM grows with CL and shrinks with sample size.
How do you find the sample mean from a confidence interval?
Average the lower and upper bounds.
How do you find the EBM from a confidence interval?
EBM = half the difference of upper and lower bounds, or upper bound – mean.
When do we use the t-distribution instead of the normal distribution?
When population σ is unknown and s (sample std dev) is used.
How is the t-score calculated?
t = (x̄ – μ) / (s/√n), follows t-distribution with df = n – 1.
What is a Population Proportion?
A proportion parameter estimated from sample proportion p̂ = x/n.
How do you calculate a confidence interval for a population proportion?
CI = p̂ ± z* × √(p̂(1 – p̂)/n).
What is the “plus four” method for small samples?
Adds 2 successes and 2 failures to improve CI accuracy for small samples.
