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Confidence Intervals for Population Mean definitions

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  • Confidence Interval
    A range of values, derived from sample data, that likely contains the true population mean with a specified confidence level.
  • Population Mean
    The average value of a variable for the entire group being studied, often represented by the Greek letter mu.
  • Sample Mean
    The average value calculated from a subset of the population, used as a point estimate for the population mean.
  • Margin of Error
    The amount added and subtracted from the sample mean to create the upper and lower bounds of a confidence interval.
  • Critical Z Value
    A cutoff point from the standard normal distribution used when the population standard deviation is known.
  • Critical T Value
    A cutoff point from the t distribution, used when the population standard deviation is unknown and estimated by the sample.
  • Population Standard Deviation
    A measure of variability for the entire population, denoted by sigma, used in confidence interval calculations when known.
  • Sample Standard Deviation
    A measure of variability within the sample, denoted by s, used to estimate the population standard deviation when unknown.
  • Degrees of Freedom
    A parameter for the t distribution, calculated as the sample size minus one, affecting the shape of the distribution.
  • Normal Distribution
    A symmetric, bell-shaped curve describing the spread of a variable, with mean zero and standard deviation one.
  • T Distribution
    A probability distribution similar to the normal distribution but wider, used when estimating the mean with unknown population standard deviation.
  • Alpha
    The probability of error in the tails of a confidence interval, calculated as one minus the confidence level.
  • Confidence Level
    The probability that the confidence interval contains the true population mean, commonly expressed as a percentage.
  • Point Estimate
    A single value, such as the sample mean, used to approximate an unknown population parameter.
  • Random Sample
    A subset of the population selected so that every member has an equal chance of being chosen, ensuring unbiased results.