Question

All assumptions needed for applying a normal approximation to the difference between two proportions in this scenario are satisfied. Find the only assumption from the list below that is unnecessary for using the normal approximation. A.The expected number of failures is greater than or equal to 10 , for both populations. B.The trials in one population is independent of the trials in the other population. C.The number of trials is the same in both groups. D.The number of trials can be assumed fixed for each group. E.The number of trials in each group is small compared with the size of their respective population. F.The probability of success is constant in each group. G.The expected number of successes is greater than or equal to 10 , for both populations.

Answer 1

The unnecessary assumption for applying normal approximation to the difference between two proportions is that the number of trials must be the same in both groups.

Step-by-step explanation:

In the context of applying a normal approximation to the difference between two proportions, certain assumptions are required to be satisfied. These include the assumption that each sample comes from a population that is normally distributed and that the two populations are independent.

The expected number of successes and failures should be greater than or equal to 10, to ensure that the distribution approximates normality. The assumption that the number of trials is the same in both groups (Choice C) is unnecessary for using the normal approximation.

What is important is that the samples are independent and large enough to satisfy the normal approximation conditions, with a sufficiently large population size in relation to the sample size to avoid over-sampling. Thus, we can conclude that the only unnecessary assumption for applying a normal approximation is that the number of trials must be the same in both groups.