Which, if any, is not a characteristic necessary for obtained values of chi-square to be distributed according to the tabled values of the chi-square distribution?
a. expected frequencies must be equal for all groups
b. the null hypothesis must be true
c. sampling must be random
d. all of the above must be true

Expected frequency of all groups in chi square test should not be equal initially to perform the test.
To help establish whether observed results are consistent with expected outcomes and to rule out the possibility that observations are the result of chance, a chi-square test is utilized.
When data are being evaluated from a random sample and the variable in issue is a categorical variable, a chi-square test is applicable.
Chi-square distributions are helpful for testing hypotheses because of how closely they resemble the conventional normal distribution.
Many significant statistical tests and theories revolve around the standard normal distribution, which is a normal distribution with a mean of zero and a variance of one.

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