Question

ch 20* we prefer the t procedures to the z procedures for inference about a population mean because
z requires that you can regard your data as an srs from the population.
z can be used only for large samples.
z requires that you know the population standard deviation σ.

Explanation:

When making inferences about a population mean, the \(z\) - procedures assume that the population standard deviation \(\sigma\) is known. In many real - world situations, the population standard deviation \(\sigma\) is unknown. The \(t\) - procedures use the sample standard deviation \(s\) to estimate the population standard deviation. Both \(z\) and \(t\) procedures require the data to be an SRS (Simple Random Sample) from the population. Also, the \(z\) - distribution can be used for both large and small samples when \(\sigma\) is known (although for small samples with known \(\sigma\) it is less common in practice as \(\sigma\) is rarely known for small - scale populations).

Answer:

\(z\) requires that you know the population standard deviation \(\sigma\).