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Confidence Intervals for Population Proportion definitions

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  • Confidence Interval
    A range of values calculated from sample data that likely contains the true population proportion with a specified level of confidence.
  • Population Proportion
    The true fraction of individuals in a population exhibiting a particular characteristic, often denoted as p.
  • Point Estimate
    A single value, calculated from sample data, used as the best guess for the population proportion.
  • Sample Size
    The total number of individuals or observations included in a sample, represented by n.
  • Margin of Error
    The maximum expected difference between the point estimate and the true population proportion, based on sample data.
  • Critical Z-Value
    A number from the standard normal distribution that corresponds to the desired confidence level, used in interval calculations.
  • Confidence Level
    The probability, expressed as a percentage, that the confidence interval contains the true population proportion.
  • Sampling Distribution
    The probability distribution of a statistic, such as p̂, calculated from repeated samples of the same size.
  • Successes
    The count of individuals in a sample exhibiting the characteristic of interest, used to compute p̂.
  • Failures
    The count of individuals in a sample not exhibiting the characteristic of interest, used to verify normality.
  • Normality Condition
    A requirement that both np and nq are at least 5, ensuring the sampling distribution of p̂ is approximately normal.
  • Lower Bound
    The smallest value in a confidence interval, calculated by subtracting the margin of error from the point estimate.
  • Upper Bound
    The largest value in a confidence interval, calculated by adding the margin of error to the point estimate.
  • One-Prop C Interval
    A calculator function on the TI-84 used to quickly compute confidence intervals for population proportions.
  • Alpha
    The probability that the confidence interval does not contain the true population proportion, equal to 1 minus the confidence level.