Which one of the following is NOT a correct formula for calculating the expected

Question

Which one of the following is NOT a correct formula for calculating the expected counts for a goodness-of-fit test? (Choose all that apply) a) E-n/k, where n is the total sample size, k is the number of categories and, if we assume that all of the expected frequencies are equal. b) E-nk, where n is the total sample size, k is the number of categories and, if we assume that all of the expected frequencies are equal. c) E-p/n, where n is the sample size, p is the observed frequency of each category and, if we do not assume that all of the expected frequencies are equal. d) E-np, where n is the total sample size, p is the observed frequency of each category and, if we do not assume that all of the expected frequencies are equal

Explanation / Answer

In case of all of the expected frequencies are equal, the expected frequency is n / k (total sample size divided by the number of categories).

In case of all of the expected frequencies are not equal, the expected frequency is np (total sample size multiplied by hypothesized proportion from the null hypothesis of each category).

So, except a), all other options are not a correct formula for calculating the expected counts for goodness of fit.

Hence the correct options are b), c) and d).

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