Question

which of the following is a requirement for testing a claim about a population proportion?

a. the trials are dependent.
b. the sample observations are a stratified sample.
c. the conditions np ≥ 5 and nq ≥ 5 are both satisfied.
d. none of the other statements are requirements for testing a claim about a population proportion.

Explanation:

When testing a claim about a population proportion, the following requirements must be met:

• The sample is a simple random sample.
• The conditions for a binomial distribution are satisfied (fixed number of trials, independent trials, two possible outcomes, constant probability of success).
• The normal distribution can be used to approximate the binomial distribution, which requires \(np\geq5\) and \(nq\geq5\) (where \(q = 1 - p\)).

Now let's analyze each option:

• Option A: For a binomial - like situation (which is used for population proportion testing), the trials should be independent. So, "The trials are dependent" is incorrect.
• Option B: A stratified sample is not a requirement for testing a population proportion. A simple random sample is the requirement.
• Option C: As mentioned above, when using the normal approximation to the binomial (a common method for testing population proportion), \(np\geq5\) and \(nq\geq5\) must be satisfied.

Answer:

C. The conditions \(np\geq5\) and \(nq\geq5\) are both satisfied.