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Performing Hypothesis Tests: Proportions definitions

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  • Population Proportion
    Represents the expected fraction of successes in the entire group being studied, often denoted by p.
  • Sample Proportion
    Calculated by dividing the number of successes in a sample by the sample size; denoted as p hat.
  • Null Hypothesis
    Assumes the population proportion equals a specified value, serving as the default claim in testing.
  • Alternative Hypothesis
    Represents the claim being investigated, often suggesting the population proportion differs from the expected value.
  • Test Statistic
    A value computed from sample data, used to assess the evidence against the null hypothesis; often a z-score.
  • Z-Score
    Measures how far the sample proportion deviates from the expected proportion, standardized by sample size.
  • P-Value
    Indicates the probability of observing a result as extreme as the sample, assuming the null hypothesis is true.
  • Significance Level
    A threshold, denoted by alpha, used to decide whether to reject the null hypothesis; common values are 0.01 or 0.05.
  • Critical Value
    A cutoff point on the test statistic scale that determines the rejection region for the null hypothesis.
  • Random Sample
    A subset of the population selected so each member has an equal chance of inclusion, ensuring unbiased results.
  • One-Proportion Z-Test
    A statistical procedure used to compare a sample proportion to a hypothesized population proportion.
  • Left-Tailed Test
    A hypothesis test where the alternative hypothesis suggests the population proportion is less than the expected value.
  • Alpha
    Represents the probability of making a Type I error, or rejecting a true null hypothesis.
  • N
    Denotes the sample size, or the total number of observations included in the analysis.
  • P Sub Zero
    The hypothesized value for the population proportion entered into calculators for hypothesis testing.