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Hypothesis Tests for Correlation Coefficient Using TI-84 definitions

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  • Correlation Coefficient
    A numerical measure indicating the strength and direction of a linear relationship between two variables in a dataset.
  • Population Correlation Coefficient
    A parameter representing the true linear relationship between two variables across an entire population.
  • Null Hypothesis
    A statement asserting no linear correlation exists between two variables, often represented by a population parameter equal to zero.
  • Alternative Hypothesis
    A claim suggesting a linear correlation exists, either in a specific direction or simply not equal to zero.
  • Significance Level
    A threshold used to determine whether evidence is strong enough to reject the null hypothesis, commonly denoted by alpha.
  • P-value
    A probability indicating how likely observed data would occur if the null hypothesis were true; compared to alpha for decision-making.
  • Linear Correlation
    A relationship where changes in one variable are associated with proportional changes in another, forming a straight-line pattern.
  • TI-84
    A graphing calculator used to perform statistical tests, including those for correlation coefficients.
  • LinReg T-Test
    A statistical function on the TI-84 that tests hypotheses about the population correlation coefficient using sample data.
  • Two-tailed Test
    A hypothesis test that considers deviations in both directions from the null value, checking for any nonzero correlation.
  • Sample Data
    A subset of values collected from a population, used to estimate parameters and test hypotheses.
  • Strong Positive Correlation
    A situation where high values of one variable are consistently associated with high values of another, indicated by a coefficient near 1.
  • Frequency
    A setting in statistical tests indicating how often each data point occurs, typically set to one for individual entries.
  • Alpha
    A chosen probability threshold for significance, below which results are considered statistically meaningful.
  • Statistical Significance
    A determination that observed results are unlikely to have occurred by chance, based on comparison of p-value and alpha.