For the provided problems, let's analyze each situation to identify the type of sampling and assess whether the sample is representative.

Scenario 1

"Elvira selects every 5th student in the lunch line to determine if students at the school are satisfied with school lunch."

1. Type of Sampling:
   This is systematic sampling because Elvira selects students at regular intervals (every 5th student).

2. Representative?:
   Whether the sample is representative depends on how students line up in the lunch line. If the order of students in the line is random, then this method can produce a representative sample. However, if certain groups of students consistently occupy specific spots in the line (e.g., early birds or those who prefer arriving late), the sample might be biased.

Scenario 2

"Elvira surveys the first 60 students in the lunch line to determine if students at the school are satisfied with school lunch."

1. Type of Sampling:
   This is convenience sampling because Elvira is sampling the first 60 students without any randomization or interval-based method.

2. Representative?:
   This sample is likely not representative of the entire population. Students who arrive first in the lunch line may have specific characteristics (e.g., they might be more punctual or have particular food preferences), which could introduce bias.

Would you like detailed explanations for any part of this?

Related Questions:

1. How does systematic sampling differ from stratified sampling?
2. What is an example of a situation where convenience sampling might be appropriate?
3. Why is randomization important in reducing bias in sampling methods?
4. Can a systematic sample ever become biased? Provide an example.
5. What statistical measures can be used to evaluate whether a sample is representative?

Tip:

Always consider the population’s diversity when evaluating whether a sampling method is representative!