Question

In Exercises 1.40 to \(1.45,\) state whether or not the sampling method described produces a random sample from the given population. The population is incoming students at a particular university. The name of each incoming student is thrown into a hat, the names are mixed, and 20 names (each corresponding to a different student) are drawn from the hat.

Short answer

Yes, the sampling method described does produce a random sample from the given population.

Step-by-step solution

Understanding a Random Sample

A random sample is a subset of individuals chosen from a larger set. Each individual is chosen randomly and entirely by chance, such that each has the same probability of being chosen at any stage during the sampling process.

Applying to the given situation

The names of all incoming students are placed in a hat. After the mixing of names, 20 are drawn. Therefore, each student has an equal chance of being selected since all their names are mixed up in the hat, implying randomness in the selection.

Drawing conclusion

Given that each student has an equal chance of being selected, the sampling method described aligns with the concept of a random sample. Thus, this method does yield a random sample from the population of incoming students at the university.