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Two Means - Sigma Known Hypothesis Test - Excel definitions

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  • Population Standard Deviation
    A known measure of spread for an entire group, used to determine variability when performing a z-test for two means.
  • Normal Distribution
    A symmetric, bell-shaped curve used as the basis for calculating probabilities in z-tests when population spread is known.
  • Z-Test
    A statistical method for comparing two means when population standard deviations are known, relying on the normal curve.
  • Null Hypothesis
    A starting assumption stating no difference exists between two group averages, often represented as equal means.
  • Alternative Hypothesis
    A claim suggesting a difference or specific direction between two group averages, such as one being less than the other.
  • Sample Mean
    An average calculated from collected data, representing the central value for each group in the test.
  • Sample Size
    The number of observations or data points collected from each group, impacting the calculation of test statistics.
  • Z-Score
    A value showing how far the observed difference between means is from zero, measured in standard error units.
  • P-Value
    A probability indicating how likely the observed data would occur if the null hypothesis were true.
  • Alpha Level
    A threshold probability, often set at 0.05, used to decide whether to reject the null hypothesis.
  • Test Statistic
    A calculated number summarizing the evidence against the null hypothesis, compared to a reference distribution.
  • Left Tail Probability
    The cumulative chance of observing a value as extreme or more extreme in the negative direction under the normal curve.
  • Cumulative Distribution
    A function giving the probability that a variable falls below a certain value, used to find p-values in Excel.
  • Numerator
    The difference between two sample averages, forming the top part of the z-score formula.
  • Denominator
    The square root of the sum of variances divided by sample sizes, forming the bottom part of the z-score formula.