Question

(e) since categorical data was collected from each observational unit, what conditions do we need to check? check all that apply.
□ ( n geq 10n ), where ( n ) is the population size (hint: this one is required!)
□ ( np geq 10 )
□ ( n geq 30 ) or normal population.
□ ( n(1 - hat{p}) geq 10 )
□ ( nhat{p} geq 10 )
□ ( sigma ) is known.
□ ( n(1 - p) geq 10 )
□ ( sigma ) is unknown.

Explanation:

The problem involves categorical data, typically analyzed using proportion tests. Key conditions for such tests include the independence assumption (ensured by \(N \geq 10n\) for sampling without replacement) and the normality approximation of the sampling distribution (requiring \(np \geq 10\) and \(n(1-p) \geq 10\) where \(p\) is the population proportion). Other options relate to mean tests (\(n \geq 30\), \(\sigma\) known/unknown) which do not apply to categorical data.

Answer:

A. \(N \geq 10n\), where \(N\) is the population size (Hint: This one is required!), D. \(n(1 - \hat{p}) \geq 10\), E. \(n\hat{p} \geq 10\), H. \(n(1 - p) \geq 10\)