Question

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

a. the sample observations are a stratified sample.
b. the conditions ( npgeq5 ) and ( nqgeq5 ) are both satisfied.
c. the trials are dependent.
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).
• \(np\geq5\) and \(nq\geq5\) (where \(q = 1 - p\)), which ensures that the normal approximation to the binomial distribution is appropriate.

Now let's analyze each option:

• Option A: A stratified sample is not a requirement for testing a population proportion. A simple random sample is what is typically required.
• Option B: The conditions \(np\geq5\) and \(nq\geq5\) are indeed requirements for using the normal approximation in testing a population proportion.
• Option C: For a binomial - like situation (which is relevant for population proportion tests), the trials should be independent.

Answer:

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