Question

which of the following is a requirement for testing a claim about a population proportion?
a. the conditions ( npgeq5 ) and ( nqgeq5 ) are both satisfied.
b. the sample observations are a stratified sample.
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 \(p\), we use the normal approximation to the binomial distribution. For this approximation to be valid, the conditions \(np\geq5\) and \(nq\geq5\) (where \(q = 1 - p\)) must be satisfied. This ensures that the sampling distribution of the sample proportion \(\hat{p}\) is approximately normal. A stratified sample is not a requirement for testing a population proportion. Also, for binomial - based tests (which are used for population proportion tests), the trials should be independent.

Answer:

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