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Sampling Distribution of Sample Proportion definitions

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  • Binomial Distribution
    A probability model for experiments with two outcomes per trial, such as success or failure, over a fixed number of trials.
  • Normal Distribution
    A symmetric, bell-shaped curve used to approximate probabilities when sample sizes are large and certain criteria are met.
  • Sample Proportion
    A value calculated by dividing the number of successes in a sample by the total number of trials, often denoted as p-hat.
  • p-hat
    A statistic representing the proportion of successes in a sample, found by dividing successes by total trials.
  • Continuity Correction
    An adjustment of 0.5 added or subtracted to a discrete variable when using a continuous distribution to approximate probabilities.
  • Z Score
    A standardized value indicating how many standard deviations a data point is from the mean in a normal distribution.
  • Standard Deviation
    A measure of the spread of a distribution, for sample proportions calculated as the square root of pq divided by n.
  • Mean
    The expected value of a distribution; for sample proportions, it equals the population probability of success.
  • n
    The total number of trials or observations in a sample or experiment.
  • p
    The probability of success on a single trial in a binomial experiment.
  • q
    The probability of failure on a single trial, calculated as one minus the probability of success.
  • Confidence Interval
    A range of values, derived from sample data, likely to contain the true population proportion with a specified probability.
  • Sampling Distribution
    The probability distribution of a statistic, such as p-hat, based on all possible random samples from a population.
  • np
    The product of sample size and probability of success, used to check if normal approximation is appropriate.
  • nq
    The product of sample size and probability of failure, also used to verify conditions for normal approximation.