Final Answer:
To accomplish their intended design of surveying approximately 150 guests through a systematic random sample of the expected 3000 guests, the venue managers should employ a systematic sampling method by selecting every 20th guest, for example, based on the total number of expected attendees.
Step-by-step explanation:
A systematic random sampling strategy involves selecting every k-th item from a list after a random start. In this case, the managers want to survey approximately 150 guests from an expected 3000 attendees. To achieve this, they can calculate the sampling interval (k) by dividing the total number of guests by the desired sample size: . This means they would select every 20th guest for the survey.
By randomly selecting a starting point, such as choosing a random number between 1 and 20 and then selecting every 20th guest thereafter, the managers ensure a systematic random sample. This method helps avoid biases that may arise from patterns in the list, providing a representative sample of guests across different zones (orchestra, grand tier, balcony).
In summary, the systematic random sampling strategy of selecting every 20th guest from the list of expected attendees ensures an unbiased and representative survey of approximately 150 guests. This approach allows the venue managers to gather insights on the overall concert experience from attendees in all three zones while efficiently managing the survey process.