Beyond representative sampling, what assumptions are needed to satisfy the requirements of a one-sample proportion test? The sample size should be at least 30 and the population have a normal distribution The sample size should be at least 30 or the population have a normal distribution $n p_{0}$ and $n q_{0}$ should both be at least 5 and the number of successes should follow a binomial distribution $n p_{0}$ and $n q_{0}$ should both be at least 5 or the number of successes should follow a binomial distribution Beyond representative sampling, what assumptions are needed to satisfy the requirements of a one-sample means test? The sample size should be at least 30 and the population have a normal distribution The sample size should be at least 30 or the population have a normal distribution $n p_{0}$ and $n q_{0}$ should both be at least 5 and the number of successes should follow a binomial distribution $n p_{0}$ and $n q_{0}$ should both be at least 5 or the number of successes should follow a binomial distribution
Solution
Step 1 ：The question is asking about the assumptions needed to satisfy the requirements of a one-sample proportion test. This is a statistical concept and does not require a Python code to solve.
Step 2 ：The one-sample proportion test is used to compare a sample proportion to a theoretical one. Beyond representative sampling, the assumptions needed to satisfy the requirements of a one-sample proportion test are: 1. The sampling method is simple random sampling. The data values must be independent of each other. 2. The number of successes (np) and the number of failures (nq) are both at least 5.
Step 3 ：So, the correct answer is "$n p_{0}$ and $n q_{0}$ should both be at least 5 and the number of successes should follow a binomial distribution".
Step 4 ：Final Answer: \(\boxed{"n p_{0}" \text{ and } "n q_{0}" \text{ should both be at least 5 and the number of successes should follow a binomial distribution}}\).
