#### Chi-square goodness-of-fit tests

Goodness-of-Fit:

We can execute a chi-square goodness-of-fit test by using the TI-82. The steps are as follows:

A) Enter the observed frequencies to the List 1.

B) Enter the expected frequencies to List 2.

i) If you are given the expected frequencies, enter them into the List 2.

ii) If you are provided probabilities, then enter the probabilities to List 2 and multiply the List 2 by the sum of List 1 and substitute List 2 with that product: sum L1 * L2 -> L2

iii) If you are testing that each and every category appear with equivalent frequency, then you can

•    Enter that value to List 2
•    Enter the total frequency to each and every value of List 2 and then divide the list by number of categories: L2/k -> L2
•    Enter 1 for each and every value in List 2 and then multiply the list by common expected frequency: L2 * E -> L2 (substitute E by the expected frequency)

C) Compute the test statistic: sum ((L1 - L2)^2 / L2)

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