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Which of the following is not a condition necessary for conducting a two-sample $z$-test for proportions?


We have a random sample from each of the two populations or from each of two different treatment groups.


The samples are independent of each other.


Each of the two populations is sufficiently larger than their respective sample size.


The total number of observations must be at least $30$ or we must know that the population distribution is approximately normal.


For each population, we expect a sufficient number of successes and a sufficient number of failures.

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