Friday, August 17, 2007

T Statistic

Student's T Statistic

Defined as:

  • t = (x_bar - mu) / (s / sqrt(n))

When to use: when a random sample of size n is chosen from a normal distribution.

Characteristics:

  • the t distribution is mound-shaped with a center at t = 0, like z;
  • it has fatter tails than z, however; it does not approach the horizontal axis as quickly as z and is not as tall in the middle; this is because t has 2 variables, the mean and sample standard deviation, whereas z has only 1 variable, the mean (the SD is set = 1).
  • Note that the larger n the more t will resemble the distribution of z; at infinitely large n values, they are identical.

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