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Two Means - Unknown, Unequal Variance definitions

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  • Null Hypothesis
    Default claim that two population means are equal, often represented as their difference being zero.
  • Alternative Hypothesis
    Statement suggesting a difference exists between two population means, challenging the default claim.
  • T-Distribution
    Probability distribution used when population standard deviations are unknown, especially with small samples.
  • Degrees of Freedom
    Value based on sample sizes, typically the smaller sample size minus one, used to reference t-tables.
  • P Value
    Probability of observing a test statistic as extreme as, or more extreme than, the one calculated, under the null.
  • Alpha
    Threshold probability for significance, often set at 0.05, used to decide whether to reject the null hypothesis.
  • Confidence Interval
    Range of values, derived from sample data, likely to contain the true difference between two population means.
  • Point Estimator
    Best guess for the difference in population means, calculated as the difference between sample means.
  • Margin of Error
    Amount added and subtracted from the point estimator to create the confidence interval, incorporating variability.
  • Sample Standard Deviation
    Measure of spread within each sample, used when population standard deviations are unknown.
  • Two-Tailed Test
    Hypothesis test where evidence for difference is considered in both directions from the null value.
  • Random Sample
    Subset of a population selected so that every member has an equal chance of being chosen, ensuring unbiased results.
  • Independence
    Condition where the outcome of one sample does not affect the outcome of the other, crucial for valid inference.
  • Critical Value
    Cutoff from the t-distribution, based on confidence level and degrees of freedom, used in margin of error calculation.
  • Pooled Variance
    Concept indicating whether variances are assumed equal; in this context, variances are not pooled.