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Two Proportions definitions

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  • Null Hypothesis
    Default assumption that two population proportions are equal, often represented as p₁ = p₂.
  • Alternative Hypothesis
    Statement suggesting a difference exists between two population proportions, such as p₁ ≠ p₂.
  • Test Statistic
    Value, typically a z-score, calculated to measure the difference between sample proportions relative to expected variation.
  • P-value
    Probability of observing a test statistic as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true.
  • Significance Level
    Threshold, often denoted alpha, used to decide whether to reject the null hypothesis, such as 0.05.
  • Confidence Interval
    Range of values, based on sample data, likely to contain the true difference between population proportions.
  • Point Estimate
    Best guess for the difference between two population proportions, calculated from sample data.
  • Margin of Error
    Amount added and subtracted from the point estimate to create the confidence interval, reflecting sampling variability.
  • Critical Value
    Z-score corresponding to the desired confidence level, used in constructing confidence intervals.
  • Pooled Proportion
    Weighted average of sample proportions, combining successes and trials from both groups for hypothesis testing.
  • Random Sampling
    Method ensuring each subject in the population has an equal chance of selection, supporting valid inference.
  • Independence
    Condition where the outcome of one sample does not affect the outcome of the other, required for valid results.
  • Successes and Failures Condition
    Requirement that each sample has at least five successes and five failures to justify normal approximation.
  • Two-tailed Test
    Hypothesis test considering deviations in both directions from the null value, often used with p₁ ≠ p₂.
  • TI-84 Calculator
    Tool used to perform hypothesis tests and construct confidence intervals for two proportions efficiently.