Final answer:
The second sampling method Millie uses, surveying every third member in her PE class (systematic sampling), is more likely to produce a representative sample compared to the first method, which may introduce bias by only surveying members in her homeroom.
Step-by-step explanation:
To determine the average number of tickets sold by the drama club at Millie's middle school, Millie can use different sampling techniques to create a representative sample. Among the methods described in the question, the first method involves surveying the club members in her homeroom, while the second method surveys every third member of the club in her physical education class.
Neither of the sampling methods described will likely produce a perfectly representative sample. However, comparing the methods raises a discussion about representativeness and bias. The first sampling method could be less representative because it only includes drama club members who are also in Millie's homeroom, which could unintentionally select for a specific group of students not representative of the entire drama club. This situation can lead to bias, as the sample might not accurately reflect the diversity of the entire club.
The second sampling method, surveying every third member of the club in her physical education class using systematic sampling, might offer a more representative sample of the drama club members, provided that the physical education class is more diverse and the members of the drama club are relatively evenly distributed in that class. This approach reduces the chance of selection bias compared to the first method, but it's still not guaranteed to be perfectly representative if the physical education class does not reflect the entire drama club's demographics.
In conclusion, while both methods have potential flaws, the second method seems more likely to produce a representative sample, assuming the diversity of the physical education class reflects the entire club.