13.3 The Chi-Square Distribution
Having rationalized the test statistic for conducting a multinomial goodness-of-fit test (Eq. 13.4), we next examine the properties of the chi-square distribution and its attendant probabilities. The chi-square distribution is a continuous distribution that represents the sampling distribution of a sum of squares of independent standard normal variables. That is, if the observations X1, . . ., Xn constitute a random sample of size n taken from a normal population with mean μ and standard deviation σ, then the Zi = (Xi − μ)/σ, i = 1, . . ., n, are independent N(0,1) random variables and
Looking to the properties of the chi-square distribution:
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