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 trials are dependent.
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 \(p\), we assume a binomial distribution for the sample data. For the normal approximation (which is often used in hypothesis - testing for proportions) to be valid, the conditions \(np\geq5\) and \(nq = n(1 - p)\geq5\) must be satisfied. A stratified sample is not a requirement for testing a population proportion. Also, for a binomial - based test (which is the basis for proportion tests), the trials should be independent.

Answer:

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