To determine which options produce a reliable random sample, let’s analyze each option:
I. Survey the first 20 students that get off the first bus - This method is not random because it only surveys students from one specific bus and could lead to bias based on the bus route or time.
II. Survey all the students in Ms. Matthew's class - This option is not random either because it only includes students from one specific class, which may not be representative of the entire school.
III. Survey every 5th student that enters the school in the morning - This method can be seen as a systematic sampling approach. If students arrive in a random manner without consistent patterns, this could yield a reasonably representative sample.
IV. Put all the students’ names in a hat and draw 20 names out - This method is truly random since each student has an equal chance of being selected.
Given this analysis, options III and IV would yield reliable random samples. So the best response is:
B. III and IV