Question

To have a binomial setting; which of the following must be true? I. When sampling; the population must be at least twenty times as large as the sample size: (Some textbooks say ten times as large:) II. Each occurrence must have the same probability of success. III: There must be a fixed number of trials.

⦁ only
⦁ and III only
⦁ and III only
⦁ II only
⦁ I,II, and III

Answer 1

For a binomial setting, a fixed number of trials (III) and a constant probability of success in each trial (II) are required. While a large population in proportion to the sample size is good practice (I), it is not a strict requirement.

Step-by-step explanation:

To have a binomial setting, the following must be true:There must be a fixed number of trials (III).Each occurrence must have the same probability of success (II).Each trial is independent of the others and conducted under identical conditions.Growing literature suggests that the population should be at least 10 or 20 times as large as the sample to prevent over-sampling and to avoid incorrect results; however, this is not a strict requirement for a binomial distribution, but more of a guideline for ensuring representativeness in sampling (I).

• The correct answer to the question is II and III only because having a sufficiently large population in relation to the sample size is a good practice for sampling representativeness but not a strict requirement for a binomial setting. What is strictly required is having a fixed number of trials where each trial has only two possible outcomes (success or failure) with the probability of success (p) being the same for each trial.