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Confidence Intervals for Population Proportion definitions

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  • Confidence Interval
    A range of values, derived from sample data, that likely contains the true value of a population parameter at a specified confidence level.
  • Population Proportion
    The true fraction or percentage of a population that possesses a certain characteristic, often denoted as p.
  • Sample Size
    The total number of observations or individuals included in a sample, represented by n.
  • Point Estimate
    A single value, calculated from sample data, used as the best guess for an unknown population parameter.
  • Margin of Error
    The maximum expected difference between the point estimate and the true population value, reflecting sampling variability.
  • Critical Z Value
    A number from the standard normal distribution that corresponds to the desired confidence level, used in interval calculations.
  • Successes
    The count of sample observations that meet the criterion of interest, such as those favoring a particular option.
  • Failures
    The count of sample observations that do not meet the criterion of interest, complementing the number of successes.
  • Confidence Level
    The probability, expressed as a percentage, that the confidence interval contains the true population parameter.
  • Sampling Distribution
    The probability distribution of a statistic, such as p-hat, based on repeated random samples from the population.
  • P-hat
    The sample proportion, calculated as the ratio of successes to the total sample size, serving as the point estimate for p.
  • Lower Bound
    The smallest value in a confidence interval, found by subtracting the margin of error from the point estimate.
  • Upper Bound
    The largest value in a confidence interval, found by adding the margin of error to the point estimate.
  • Alpha
    The probability that the confidence interval does not contain the true population parameter, equal to one minus the confidence level.
  • One-Prop Z Interval
    A calculator function that computes a confidence interval for a population proportion using sample data and a specified confidence level.