Key Terms

degrees of freedom (df)
the number of objects in a sample that are free to vary
pooled proportion
estimate of the common value of p1 and p2
standard deviation
a number that is equal to the square root of the variance and measures how far data values are from their mean; notation: s for sample standard deviation and σ for population standard deviation
variable (random variable)
a characteristic of interest in a population being studied

Common notation for variables are uppercase Latin letters X, Y, Z,... Common notation for a specific value from the domain (set of all possible values of a variable) are lowercase Latin letters x, y, z,.... For example, if X is the number of children in a family, then x represents a specific integer 0, 1, 2, 3, .... Variables in statistics differ from variables in intermediate algebra in two ways:
  • The domain of the random variable (RV) is not necessarily a numerical set; the domain may be expressed in words; for example, if X = hair color, then the domain is {black, blond, gray, green, orange}.
  • We can tell what specific value x of the random variable X takes only after performing the experiment.