Questions: Decide whether the sampling method could result in a biased sample. Explain your reasoning. 16. On the first day of school, all of the incoming freshmen attend an orientation program. The principal wants to learn the opinions of the freshmen regarding the orientation program. He decides to ask the first 25 freshmen that he sees. 17. The manager of an apartment building wants to know if the residents are satisfied with his service. He writes each apartment number on a piece of paper and places the pieces of paper in a hat. Then he randomly chooses 10 apartment numbers and asks the residents of the 10 apartments about his service. 18. The members of the school drama club want to know how much students are willing to pay for a ticket to one of their productions. They decide that each member of the drama club should ask five of his or her friends what they are each willing to pay:

Let's analyze each sampling method to determine if it could result in a biased sample and explain the reasoning behind each conclusion.

The answer is: Yes, this sampling method could result in a biased sample.

Explanation:

• Selection Bias: The first 25 freshmen seen by the principal may not be representative of the entire freshman class. These students might share certain characteristics (e.g., arriving early, being more punctual, or more eager) that are not representative of the entire population of freshmen.
• Non-Random Sampling: This method does not use random sampling, which increases the likelihood of bias. A more representative approach would be to randomly select freshmen from the entire group attending the orientation.

The answer is: No, this sampling method is unlikely to result in a biased sample.

Explanation:

• Random Sampling: By writing each apartment number on a piece of paper and randomly selecting 10, the manager ensures that every apartment has an equal chance of being chosen. This method minimizes selection bias.
• Representative Sample: Random sampling generally leads to a sample that is representative of the population, assuming the sample size is sufficiently large. In this case, 10 apartments out of a larger number should provide a reasonable cross-section of opinions.

The answer is: Yes, this sampling method could result in a biased sample.

Explanation:

• Selection Bias: Drama club members asking their friends introduces a significant risk of bias. Friends of drama club members may have similar interests, socioeconomic backgrounds, or attitudes towards the drama club, which may not reflect the broader student population.
• Non-Random Sampling: This method does not use random sampling, which increases the likelihood of bias. A more representative approach would be to randomly select students from the entire student body to get a more accurate measure of willingness to pay for tickets.

In summary, the sampling methods in questions 16 and 18 are likely to result in biased samples due to selection bias and non-random sampling. The method in question 17, however, uses random sampling and is less likely to result in a biased sample.